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2000 Fiscal Year Final Research Report Summary

Combinatorial Methods for Discrete Geometry

Research Project

Project/Area Number 10304008
Research Category

Grant-in-Aid for Scientific Research (A).

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNIHON UNIVERSITY

Principal Investigator

SAITO Akira  Nihon Univ., Dept. of Applied Mathematics, Professor, 文理学部, 教授 (90186924)

Co-Investigator(Kenkyū-buntansha) KANO Mikio  Ibaraki Univ., Dept of Information Engineering, Professor, 工学部, 教授 (20099823)
ENOMOTO Hikoe  Keio Univ., Dept. of Mathematics, Professor, 理工学部, 教授 (00011669)
MAEHARA Hiroshi  Ryukyu Univ., Dept. of Mathematics, Professor, 教育学部, 教授 (60044921)
OTA Katsuhiro  Keio Univ., Dept. of Mathematics, Associate Preofessor, 理工学部, 助教授 (40213722)
KANEKO Atsushi  Kogakuin Univ., Dept. of Computer Science, Associate Professor, 工学部, 助教授 (30255608)
Project Period (FY) 1998 – 2000
Keywordsdiscrete geometry / combinatorics / triangulation / quadrangulation / graph theory / tree / straight-line embedding / network flow
Research Abstract

In this project, we first extracted the combinatorial aspects from a number of problems in discrete geometry, and categorized them. Then by invetigating each category, we tried to establish general methods which are applicable to discrete geometry. The following are some of the most successful results in this project.
・ In discrete geometry, there are a number of problems which are essentially equivalent to joining points by straight line segments so that the resulting geometric object becomes a hamiltonian cycle embedded in the plane and that it has the least number of crossing of line segments. We proved that they are combinatorial problems in essence, and established a combinatorial method to tackle them.
・ We proved that the problems of independent geometric trees can be handled as an extension of independent trees in graphs, and we establlished a graph-theoretic approach to address these problems.
・ In discrete geomtery, there are many problems on dividing an Euclidean space with a finite number of geometric objects by a hyperplane so that both divided half-spaces contain almost the same number of the objects. We studied the combinatorial aspects of these problems, and solved the problem in which each object is a ball.
・ We proved that there are many problems in discrete geometry which are essentially graph decomposition problems. We solved a number of these decomposition problems, especially in case of complete graphs and complete bipartite graphs.
The above results are just a small fraction of our entire results, which are described fully in the project report. Considering the quantity of the quality of the result, we believe that this project was extremely successful.

  • Research Products

    (198 results)

All Other

All Publications (198 results)

  • [Publications] Hiroshi Maehara: "A variation to the ruin problem"Mathematica Japonica. 47. 97-102 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "A minimal rigid graph in the plane that is not constructible by ruler and compass"Yokohama Math.J.. 45. 109-111 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "Is there a cicle that passes through a given number of lattice points?"European J.Combinatorics. 19. 591-592 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "Embedding a set of rational points in lower dimensions"Discrete Mathematics. 192. 273-279 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "Vector fields and quadratic surfaces"Ryukyu Math.J.. 11. 53-63 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Mamoru Watanabe: "String decompositions of graphs"Ars Combinatoria. 49. 225-236 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "On the existence of disjoint cycles in a graph"Combinatorica. 18. 487-492 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "Toughness and the existence of κ-factors III"Discrete Mathematics. 189. 277-282 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "Pyramidal tours with step-backs and the asymmetric traveling salesman problem"Discrete Applied Mathematics. 87. 57-65 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "Super edge-magic graphs"SUT J.Math.. 34. 105-109 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "A note on difference sets"J.Combinatorial Theory (A). 84. 133-144 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Mikio Kano: "A[κ,κ+1]-factor containing given hamiltonian cycle"Science in China (A). 41. 933-988 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Morimasa Tsuchiya: "On uniform intersection numbers"Ars Combinatoria. 48. 225-232 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Makoto Mori: "Low discrepancy sequences generated by piecewise linear maps"Monte Carlo Methods and Applications. 4. 141-162 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tetsuo Asano: "Topological walk revisited"IEICE Trans. Fundamentals. E81-A. 751-756 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tetsuo Asano: "Contour representation of an image with applications"Trans. IPS of Japan. 39. 3242-3251 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Norihide Tokushige: "Some inequalities concerning cross-intersecting families"Combinatorics, Probability & Computing. 7. 247-260 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Seiya Negami: "Ramsey-type theorems for spatial graphs and good drawings"J.Combinatorial Theory (B). 72. 53-62 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Seiya Negami: "Diagonal flips in triangulations of closed surfaces, estimating upper bounds"Yokohama Math.J.. 45. 113-124 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kimihiko Motegi: "Applications of graph theory to cut-and-paste arguments"Sugaku Expositions. 11. 123-143 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kimihiko Motegi: "Seifert fibered manifolds and Dehn surgery II"Math.Ann.. 311. 647-664 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Atsushi Kaneko: "On decomposition of triangle-free graphs under degree constraints"J.Graph Theory. 27. 7-9 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Imai: "OBDDs of a monotone function and its prime implicants"Theory of Computing Systems. 31. 579-591 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Akira Saito: "Closure and hamiltonian-connectivity of claw-free graphs"Discrete Mathematics. 195. 67-80 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Akira Saito: "Long paths, long cycles and their relative length"J.Graph Theory. 30. 91-99 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Akira Saito: "Degree sums and graphs that are not covered by two cycles"J.Graph Theory. 32. 51-61 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Akira Saito: "Neighborhood unions and factor-critical graphs"Discrete Mathematics. 205. 217-220 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Akira Saito: "Closure, 2-factors and cycle coverings in claw-free graphs"J.Graph Theory. 32. 109-117 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "On the number of acute triangles in a straight-line embedding of a maximal planar graph"J.Combinatorial Theory (B). 75. 110-115 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "Lexell's theorem via an inscribed angle theorem"Amer.Math.Monthly. 106. 352-352 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "On knotted necklace of pearls"European J.Combinatorics. 20. 411-420 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "Geometry of frameworks"Yokohama Math.J.. 47. 41-65 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "Configuration spaces of pentagonal frameworks"European J.Combinatorics. 20. 839-844 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "Arranging solid balls on a table to make a κ-component link"Ryukyu Math.J.. 12. 31-35 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "Embedding graphs into a three page book with O (M log N) crossing of edges over a spine"SIAM J.Discrete Mathematics. 12. 337-341 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "Extremal 2-connected graphs with given diameter"Tokyo J.Math.. 22. 1-16 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "Lower bound for the number of edge-crossing over the spine in a topological book embedding of a graph"Discrete Applied Mathematics. 92. 149-155 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "Connected subgraphs with small degree sums in 3-connected planer graphs"J.Graph Theory. 30. 191-203 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Atsushi Kaneko: "Balanced partitions of two sets of points in the plane"Computational Geometry : Theory and Applications. 13. 253-261 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Atsushi Kaneko: "A straight-line embedding of two rooted trees in the plane"Discrete and Computational Geometry. 21. 603-613 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kazuhiko Ushio: "S^^<^>_κ-factorization of symmetric complete tripartite digraphs"Discrete Mathematics. 197/198. 791-797 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kazuhiko Ushio: "Cycle-factorization of symmetric complete multipartite digraphs"Discrete Mathematics. 199. 273-278 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kazuhiko Ushio: "Semi-evenly partite star-factorization of symmetric complete tripartite digraphs"Australasian J. Combinarorics. 20. 69-75 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kazuhiko Ushio: "Bigraph-factorization of symmetric complete bipartite multi-digraphs"Australasian J. Combinatorics. 20. 261-265 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Morimasa Tsuchiya: "On intersection numbers, total clique covers and regular graphs"J.Combinatorial Computing and Combinatorial Mathematics. 30. 33-43 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Morimasa Tsuchiya: "On upper bound graphs with respect to line graphs"Southeast Asian Bulletin of Mathematics. 23. 265-269 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Makoto Mori: "Fredholm determinant for higher dimensional piecewise linear transformations"Japanese J.Math.. 25. 317-342 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Makoto Mori: "Discrepancy of sequences generated by piecewise monotone maps"Monte Carlo Methods and Application. 5. 55-68 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tetsuo Asano: "Digital halftoning algorithms based on random space-filling curve"IEICE Trans.Fundamentals. E82-A. 553-556 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Katsuhiro Ota: "Vertex-disjoint claws in graphs"Discrete Mathematics. 197/198. 225-246 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Norihide Tokushige: "Erdos-Ko-Rado theorem for integer sequences"Combinatorica. 19. 55-63 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Seiya Negami: "Diagonal flips in triangulations on closed surfaces with minimum degree at least four"J.Combinatorial Theory (B). 76. 68-92 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Seiya Negami: "Constructing the graphs that triangulate both the torus and the Klein bottle"J.Combinatorial Theory (B). 77. 211-218 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Seiya Negami: "Diagonal flips of triangulations on surfaces, survey"Yokohama Math.J.. 47. 1-40 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Seiya Negami: "Note on frozen triangulations on closed surfaces"Yokohama Mth.J.. 47. 191-202 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Seiya Negami: "Diagonal flips in pseudo-triangulations of closed surfaces without loops"Yokohama Math.J.. 47. 213-223 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Seiya Negami: "Every 5-connected triangulations of the Klein bottle is hamiltonian"Yokohama Math.J.. 47. 239-244 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kimihiko Motegi: "Toroidal and annular Dehn surgeries of solid tori"Topology and its Applications. 93. 173-178 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kimihiko Motegi: "Seifert fibered manifolds and Dehn surgery III"Comm.Anal.Geom.. 7. 551-582 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Atsushi Kaneko: "The connectivities of leaf graphs of 2-connected graphs"J.Combinatorial Theory (B). 76. 155-169 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Atsushi Kaneko: "A degree condition for the existence of a 1-factor in graphs or their complements"Discrete Mathematics. 203. 1-8 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Imai: "Maxmin location of convex objects in a polygon and related dynamic Voronoi diagrams"J.Oper.Res.Soc.Japan. 42. 45-58 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Imai: "Enhanced A^* algorithms for multiple alignment : optimal alignments for several sequences and κ-opt approximate alignments for large cases"Theoretical Computer Science. 210. 341-374 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Imai: "Optimality and integer programming formulations of triangulations"Trans. Inform. Process. Soc. Japan. 40. 2861-2871 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Atsuhiro Nakamoto: "Transformations in closed 2-cell embeddings on surfaces preserving specified properties"Discrete Mathematics. 197/198. 607-615 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Atsuhiro Hakamoto: "Generating quadrangulations of surfaces with minimum degree at least three"J.Graph.Theory. 30. 223-234 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Atsuhiro Nakamoto: "The YΔ-equivalence of kernels on the torus without taking duals"Yokohama Math.J.. 47. 183-190 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "Oriented graphs generated by random points on a circle"J.Applied Probability. 37. 534-539 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "On the waiting time in a janken game"J.Applied Probability. 37. 601-605 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Mamoru Watanabe: "Cycle reversals in oriented plane quadrangulations and orthogonal plane partitions"J.Geometry. 68. 200-208 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "Graph decompositions and D_3-paths with a prescribed endvertex"Discete Mathematics. 213. 87-104 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "Induced graph theorem on magic valuations"Ars Combinatoria. 56. 25-32 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "Piercing balls sitting on a table by a vertical line"European J.Combinatorics. 21. 509-517 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "Oriented graphs generated by random points on a circle"J.Applied Probability. 37. 534-539 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "On the waiting time in a janken game"J.Applied Probability. 37. 601-605 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Mamoru Watanabe: "Cycle reversals in oriented plane quadrangulations and orthogonal plane partitions"J.Geometry. 68. 200-208 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "Graph decompositions and D_3-paths with a prescribed endvertex"Discrete Mathematics. 213. 87-104 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "Induced graph theorem on magic valuations"Ars Combinatoria. 56. 25-32 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "Toughness and the existence of κ-factors IV"Discrete Mathematics. 216. 111-120 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "Complete-factors and f-factors"Discrete Mathematics. 220. 239-242 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hikoe Enomoto: "Partitions of a graph into paths with prescribed endvertices and lengths"J.Graph Theory. 34. 163-169 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Mikio Kano: "Alternating hamiltonian cycles with minimum number of crossings in the plane"International J.Computational Geometry and Applications. 10. 73-78 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Mikio Kano: "Straight line embeddings of rooted star forests in the plane"Discrete Applied Mathematics. 101. 167-175 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Mikio Kano: "Radical perfect partitions of convex sets in the plane"Lecture Notes in Computer Science. 1763. 1-13 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kazuhiko Ushio: "S^^<^>_κ-factorization of symmetric complete tripartite digraphs"Discrete Mathematics. 211. 281-286 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kazuhiko Ushio: "Star-factorization of symmetric complete complete bipartite multi-digraphs"Discrete Mathematics. 215. 293-297 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kazuhiko Ushio: "Evenly partite bigraph-factorzation of symmetric complete tripartite digraphs"Australasian J.Combinatorics. 21. 245-250 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kazuhiko Ushio: "C^^<^>_κ-factorization of symmetric complete bipartite and tripartite multi-digraphs"Discrete Mathematics. 223. 393-397 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Morimasa Tsuchiya: "On upper bound graphs with respect to operations on graphs"Theoretical Computer Science. 235. 219-223 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Makoto Mori: "Higher order mixing property of piecewise linear transformations"Discrete and Continuous Dynamical Systems. 6. 915-934 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tetsuo Asano: "Algorithmic considerations on the computational complexities of digital line extraction problem"Trans. IEICE of Japan. J83-D-I. 80-89 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tetsuo Asano: "Effective use of geometric information for clustering and related topics"IEICE Trans. Fundamentals. E83-D. 418-427 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Katushiro Ota: "On minimally (n, λ)-connected graphs"J.Combinatorial Theory (B). 80. 156-171 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Seiya Negami: "5-Connected planar triangulations quadrangulating other surfaces"Yokohama Math.J.. 47. 187-193 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kimihiko Motegi: "Toroidal surgery on periodic knots"Pacific J.Math.. 193. 381-396 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Atsushi Kaneko: "On spanning trees with restricted degrees"Infromation Processing Letters. 73. 163-165 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Atsushi Kaneko: "Contractible edges in κ-connected graphs containg no K^-_4"SUT J.Math.. 36. 99-103 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Imai: "A path-exchange-type local search algorithm for vehicle routing and its efficient search strategy"J.Oper.Res.So.Japan. 43. 197-208 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Atsuhiro Nakamoto: "Diagonal flips in outer-torus triangulations"Discrete Mathematics. 216. 71-83 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hiroshi Maehara: "A variation to the ruin problem"Mathematica Japonica. 47. 97-102 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "A minimal rigid graph in the plane that is not constructible by ruler and compass"Yokohama Math.J.. 45. 109-111 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "Is there a cicle that passes through a given number of lattice points?"European J.Combinatorics. 19. 591-592 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "Embedding a set of rational points in lower dimensions"Discrete Mathematics. 192. 273-279 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "Vector fields and quadratic surfaces"Ryukyu Math.J.. 11. 53-63 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Mamoru Watanabe: "String decompositions of graphs"Ars Combinatoria. 49. 225-236 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "On the existence of disjoint cycles in a graph"Combinatorica. 18. 487-492 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "Toughness and the existence of k-factors III"Discrete Mathematics. 189. 277-282 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "Pyramidal tours with step-backs and the asymmetric traveling salesman problem"Discrete Applied Mathematics. 87. 57-65 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "Super edge-magic graphs"SUT J.Math.. 34. 105-109 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "A note on difference sets"J.Combinatorial Theory (A). 84. 133-144 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Mikio Kano: "A [k, k+1]-factor containing given hamiltonian cycle"Science in China (A). 41. 933-988 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Morimasa Tsuchiya: "On uniform intersection numbers"Ars Combinatoria. 48. 225-232 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Makoto Mori: "Low discrepancy sequences generated by piecewise linear maps"Monte Carlo Methods and Applications. 4. 141-162 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tetsuo Asano: "Topological walk revisited"IEICE Trans.Fundamentals. E81-A. 751-756 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tetsuo Asano: "Contour representation of an image with applications"Trans.IPS of Japan. 39. 3242-3251 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Norihide Tokushige: "Some inequalities concerning cross-intersecting families"Combinatorics, Probability & Computing. 7. 247-260 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Seiya Negami: "Ramsey-type theorems for spatial graphs and good drawings"J.Combinatorial Theory (B). 72. 53-62 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Seiya Negami: "Diagonal flips in triangulations of closed surfaces, estimating upper bounds"Yokohama Math.J.. 45. 113-124 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kimihiko Motegi: "Applications of graph theory to cut-and-paste arguments"Sugaku Expositions. 11. 123-143 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kimihiko Motegi: "Seifert fibered manifolds and Dehn surgery II"Math.Ann.. 311. 647-664 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Atsushi Kaneko: "On decomposition of triangle-free graphs under degree constraints"J.Graph Theory. 27. 7-9 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Imai: "OBDDs of a monotone function and its prime implicants"Theory of Computing Systems. 31. 579-591 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Akira Saito: "Closure and hamiltonian-connectivity of claw-free graphs"Discrete Mathematics. 195. 67-80 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Akira Saito: "Long paths, long cycles and their relative length"J.Graph Theory. 30. 91-99 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Akira Saito: "Degree sums and graphs that are not covered by two cycles"J.Graph Theory. 32. 51-61 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Akira Saito: "Neighborhood unions and factor-critical graphs"Discrete Mathematics. 205. 217-220 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Akira Saito: "Closure, 2-factors and cycle coverings in claw-free graphs"J.Graph Theory. 32. 109-117 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "On the number of acute triangles in a straightline embedding of a maximal planar graph"J.Combinatorial Theory (B). 75. 110-115 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "Lexell's theorem via an inscribed angle theorem"Amer.Math.Monthly. 106. 352-353 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "On knotted necklace of pearls"European J.Combinatorics. 20. 411-420 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "Geometry of frameworks"Yokohama Math.J.. 47. 41-65 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "Configuration spaces of pentagonal frameworks"European J.Combinatorics. 20. 839-844 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "Arranging solid balls on a table to make a k-component link"Ryukyu Math.J.. 12. 31-35 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "Embedding graphs into a three page book with O(M log N) crossing of edges over a spine"SIAM J.Discrete Mathematics. 12. 337-341 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "Extremal 2-connected graphs with given diameter"Tokyo J.Math.. 22. 1-16 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "Lower bound for the number of edge-crossing over the spine in a topological book embedding of a graph"Discrete Applied Mathematics. 92. 149-155 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "Connected subgraphs with small degree sums in 3-connected planar graphs"J.Graph Theory. 30. 191-203 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Atsushi Kaneko: "Balanced partitions of two sets of points in the plane"Computational Geometry : Theory and Applications. 13. 253-261 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Atsushi Kaneko: "A straight-line embedding of two rooted trees in the plane"Discrete and Computational Geometry. 21. 603-613 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kazuhiko Ushio: "S_k-factorization of symmetric complete tripartite digraphs"Discrete Mathematics. 197/198. 791-797 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kazuhiko Ushio: "Cycle-factorization of symmetric complete multipartite digraphs"Discrete Mathematics. 199. 273-278 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kazuhiko Ushio: "Semi-evenly partite star-factorization of symmetric complete tripartite digraphs"Australasian J.Combinarorics. 20. 69-75 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kazuhiko Ushio: "Bigraph-factorization of symmetric complete bipartite multi-digraphs"Australasian J.Combinatorics. 20. 261-265 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Morimasa Tsuchiya: "On intersection numbers, total clique covers and regular graphs"J.Combinatorial Computing and Combinatorial Mathematics. 30. 33-43 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Morimasa Tsuchiya: "On upper bound graphs with respect to line graphs"Southeast Asian Bulletin of Mathematics. 23. 265-269 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Makoto Mori: "Fredholm determinant for higher dimensional piecewise linear transformations"Japanese J.Math.. 25. 317-342 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Makoto Mori: "Discrepancy of sequences generated by piecewise monotone maps"Monte Carlo Methods and Application. 5. 55-68 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tetsuo Asano: "Digital halftoning algorithms based on random space-filling curve"IEICE Trans.Fundamentals. E82-A. 553-556 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Katsuhiro Ota: "Vertex-disjoint claws in graphs"Discrete Mathematics. 197/198. 225-246 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Norihide Tokushige: "Erdos-Ko-Rado theorem for integer sequences"Combinatorica. 19. 55-63 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Seiya Negami: "Diagonal flips in triangulations on closed surfaces with minimum degree at least four"J.Combinatorial Theory (B). 76. 68-92 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Seiya Negami: "Constructing the graphs that triangulate both the torus and the Klein bottle"J.Combinatorial Theory (B). 77. 211-218 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Seiya Negami: "Diagonal flips of triangulations on surfaces, survey"Yokohama Math.J.. 47. 1-40 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Seiya Negami: "Note on frozen triangulations on closed surfaces"Yokohama Mth.J.. 47. 191-202 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Seiya Negami: "Diagonal flips in pseudo-triangulations of closed surfaces without loops"Yokohama Math.J.. 47. 213-223 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Seiya Negami: "Every 5-connected triangulations of the Klein bottle is hamiltonian"Yokohama Math.J.. 47. 239-244 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kimihiko Motegi: "Toroidal and annular Dehn surgeries of solid tori"Topology and its Applications. 93. 173-178 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kimihiko Motegi: "Seifert fibered manifolds and Dehn surgery III"Comm. Anal.Geom.. 7. 551-582 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Atsushi Kaneko: "The connectivities of leaf graphs of 2-connected graphs"J.Combinatorial Theory (B). 76. 155-169 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Atsushi Kaneko: "A degree condition for the existence of a 1-factor in graphs or their complements"Discrete Mathematics. 203. 1-8 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Imai: "Maxmin location of convex objects in a polygon and related dynamic Voronoi diagrams"J.Oper.Res.Soc.Japan. 42. 45-58 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Imai: "Enhanced A^* algorithms for multiple alignment : optimal alignments for several sequences and k-opt approximate alignments for large cases"Theoretical Computer Science. 210. 341-374 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Imai: "Optimality and integer programming formulations of triangulations"Trans.Inform.Process.Soc.Japan. 40. 2861-2871 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Atsuhiro Nakamoto: "Transformations in closed 2-cell embeddings on surfaces preserving specified propeties"Discrete Mathematics. 197/198. 607-615 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Atsuhiro Hakamoto: "Generating quadrangulations of surfaces with minimum degree at least three"J.Graph Theory. 30. 223-234 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Atsuhiro Nakamoto: "The YΔ-equivalence of kernels on the torus without taking duals"Yokohama Math.J.. 47. 183-190 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Akira Saito: "Closure and factor-critical graphs"Discrete Mathematics. 215. 171-179 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "Oriented graphs generated by random points on a circle"J.Applied Probability. 37. 534-539 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "On the waiting time in a janken game"J.Applied Probability. 37. 601-605 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Mamoru Watanabe: "Cycle reversals in oriented plane quadrangulations and orthogonal plane partitions"J.Geometry. 68. 200-208 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "Graph decompositions and D_3-paths with a prescribed endvertex"Discrete Mathematics. 213. 87-104 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "Induced graph theorem on magic valuations"Ars Combinatoria. 56. 25-32 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "Piercing balls sitting on a table by a vertical line"European J.Combinatorics. 21. 509-517 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "Oriented graphs generated by random points on a circle"J.Applied Probability. 37. 534-539 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Maehara: "On the Waiting time in a janken game"J.Applied Probability. 37. 601-605 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Mamoru Watanabe: "Cycle reversals in oriented plane quadrangulations and orthogonal plane partitions"J.Geometry. 68. 200-208 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "Graph decompositions and D_3-paths with a prescribed endvertex"Discrete Mathematics. 213. 87-104 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "Induced graph theorem on magic valuations"Ars Combinatoria. 56. 25-32 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "Toughness and the existence of k-factors IV"Discrete Mathematics. 216. 111-120 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "Complete-factors and f-factors"Discrete Mathematics. 220. 239-242 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hikoe Enomoto: "Partitions of a graph into paths with prescribed endvertices and lengths"J.Graph Theory. 34. 163-169 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Mikio Kano: "Alternating hamiltonian cycles with minimum number of crossings in the plane"International J.Computational Geometry and Applications. 10. 73-78 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Mikio Kano: "Straight line embeddings of rooted star forests in the plane"Discrete Applied Mathematics. 101. 167-175 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Mikio Kano: "Radical perfect partitions of convex sets in the plane"Lecture Notes in Computer Science. 1763. 1-13 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kazuhiko Ushio: "S^^-_k-factorization of symmetric complete tripartite digraphs"Discrete Mathematics. 211. 281-286 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kazuhiko Ushio: "Star-factorization of symmetric complete bipartite multi-digraphs"Discrete Mathematics. 215. 293-297 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kazuhiko Ushio: "Evenly partite bigraph-factorzation of symmetric complete tripartite digraphs"Australasian J.Combinatorics. 21. 245-250 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kazuhiko Ushio: "C^^-_k-factorization of symmetric complete bipartite and tripartite multi-digraphs"Discrete Mathematics. 223. 393-397 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Morimasa Tsuchiya: "On upper bound graphs with respect to operations on graphs"Theoretical Computer Science. 235. 219-223 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Makoto Mori: "Higher order mixing property of piecewise linear transformations"Discrete and Continuous Dynamical Systems. 6. 915-934 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tetsuo Asano: "Algorithmic considerations on the computational complexities of digital line extraction problem"Trans.IEICE of Japan. J83-D-I. 80-89 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tetsuo Asano: "Effective use of geometric information for clustering and related topics"IEICE Trans.Fundamentals. E83-D. 418-427 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Katsuhiro Ota: "On minimally (n, λ)-connected graphs"J.Combinatorial Theory (B). 80. 156-171 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Seiya Negami: "5-Connected planar triangulations quadrangulating other surfaces"Yokohama Math.J.. 47. 187-193 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kimihiko Motegi: "Toroidal surgery on periodic knots"Pacific J.Math.. 193. 381-396 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Atsushi Kaneko: "On spanning trees with restricted degrees"Information Processing Letters. 73. 163-165 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Atsushi Kaneko: "Contractible edges in k-connected graphs containg no K^-_4"SUT J.Math.. 36. 99-103 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi Imai: "A path-exchange-type local search algorithm for vehicle routing and its efficient search strategy"J.Oper.Res.So.Japan. 43. 197-208 (2000)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2002-03-26  

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