1999 年度実績報告書

離散幾何における組合せ論的手法

研究課題

研究課題/領域番号	10304008
研究機関	日本大学
研究代表者	斎藤明日本大学, 文理学部, 教授 (90186924)
研究分担者	金子篤司工学院大学, 助教授 (30255608) 渡辺守倉敷芸術科学大学, 産業科学技術学部, 教授 (90068916) 前原濶琉球大学, 教育学部, 教授 (60044921) 太田克弘慶應義塾大学, 理工学部, 助教授 (40213722) 榎本彦衛慶應義塾大学, 理工学部, 教授 (00011669)
キーワード	離散幾何 / 組合せ論 / 木 / 四角形分割 / 閉包 / 因子 / 分割問題 / グラフ理論
研究概要	本研究は3年という期間の中で離散幾何における組合せ論的手法を発展させ、方法論として確立することを目的としている。本年度はその2年目に当たり、離散幾何の各問題の組合せ論的側面を抽出する一方、既に抽出されている問題を解決し、一般的な方法論へと展開させることを目指した。以下にその研究成果の代表的なものを挙げる。・グラフの独立木問題の離散幾何への発展形として考えられている、幾何学的独立木の各問題について、これらが強い組合せ論的特性を持つことを明らかにし、それらを扱う一般的な手法を開発した。・昨年度の研究では、閉曲面の三角形分割を調べる手法として対角変形という操作を開発し、その有効性を示したが、本年度は閉曲面の四角形分割について同様の変形操作を考え、それが染色数を調べる際に極めて強力な手段となることを示した。・離散幾何では、ユークリッド空間に置かれた有限個の幾何的対象に対し、その両側にほぼ同数が分布するような超平面(超平面でほぼ同数に分割する)の存在を問う問題が多数存在する。本年度の研究では、対象が球面である場合について、一般的な解を得た。・離散幾何の問題はグラフの因子問題に帰着することが多い。本年度の研究において、ハミルトン性を調べる手法として知られている閉包操作が、因子を調べる際にも強力な道具になり得ることを示した。本研究では、その他にも多くの知見が得られており、2年度の研究の目的は達せられたと考えられる。

研究成果

(34件)

すべてその他

すべて文献書誌 (34件)

[文献書誌] H.Komuro,A.Nakamoto and S.Negami: "Diagonal flips in triangulations of closed surfaces with minimum degree at least 4"J.Combinatorial Theory,Ser.B. 76. 68-92 (1999)
[文献書誌] S.Lawrencenko and S.Negami: "Constructing the graphs that triangulate both the torus and the Klein bottle"J.Combinatorial Theory,Ser.B. 77. 211-218 (1999)
[文献書誌] S.Negami: "Diagonal flips of triangulations on surfaces,a survey"Yokohama Math.J.. 47. 1-40 (1999)
[文献書誌] S.Negami: "Note on frozen triangulations on closed surfaces"Yokohama Math.J.. 47. 191-202 (1999)
[文献書誌] T.Watanabe and S.Negami: "Diagonal flips in pseudo-triangulations of closed surfaces without loops"Yokohama Math.J.. 47. 213-223 (1999)
[文献書誌] R.Brunet,A.Nakamoto and S.Negami: "Every 5-connected triangulations of the Klein bottle is hamiltonian"Yokohama Math.J.. 47. 239-244 (1999)
[文献書誌] H.Imai,K.Sekine and K.Imai: "Computational investigations of all-terminal network reliability via BDDs"IEICE Trans.Fundamentals. E82-A. 714-721 (1999)
[文献書誌] 田島玲,今井浩: "三角形分割の最適性と整数計画による定式化"情報処理学会論文誌. 40. 2861-2871 (1999)
[文献書誌] H.Imai and M.Inaba: "Geometric clustering by divergence and its underlyingdiscrete proximity structures"IEICE Trans.Information and Systems. E83-D. 27-35 (2000)
[文献書誌] H.Maehara: "Lexell's theorem via an inscribed angle theorem"Amer.Math.Monthly. 106. 352-352 (1999)
[文献書誌] H.Maehara and A.Oshiro: "On Knotted necklaces of pearls"European J.Combinatorics. 20. 411-420 (1999)
[文献書誌] H.Maehara: "Geometry of frameworks"Yokohama Math.J.. 47. 41-65 (1999)
[文献書誌] H.Maehara: "Configuration spaces of pentagonal frameworks"European J.Combinatorics. 20. 839-844 (1999)
[文献書誌] H.Maehara and H.Noha: "Arranging solid balls on a table to make a k-component link"Ryukyu Math.J.. 12. 31-35 (1999)
[文献書誌] H.Enomoto and K.Ota: "Connected subgraphs with small degree sums in 3-connected planar graphs"J.Graph Theory. 30. 191-203 (1999)
[文献書誌] H.Enomoto,M.S,Miyauchi and K.Ota: "Lower bounds for the number of edge-crossings over the spine in a topological book embedding of a graph"Discrete Applied Mathematics. 92. 149-155 (1999)
[文献書誌] H.Enomoto and Y.Usami: "Extremal 2-connected graphs with given diameter"Tokyo J.Math.. 22. 1-16 (1999)
[文献書誌] H.Enomoto and M.S.Miyauchi: "Embedding graphs into a three page book with O(mlogn)crossings of edges over the spine"SIAM J.Discrete Mathematics. 12. 337-341 (1999)
[文献書誌] Y.Egawa and K.Ota: "Vertex-disjoint claws in graphs"Discrete Mathematics. 197/198. 225-246 (1999)
[文献書誌] K.Ushio: "S^^<^>_k-factorization of symmetric complete tripartite digraphs"Discrete Mathematics. 197/198. 791-797 (1999)
[文献書誌] K.Ushio: "Cycle-factorization of symmetric complete multipartite digraphs"Discrete Mathematics. 199. 273-278 (1999)
[文献書誌] K.Ushio: "Semi-evenly partite star-factorization of symmetric complete tripartite digraphs"Australasian J.Combinatorics. 20. 69-75 (1999)
[文献書誌] K.Ushio: "Bigraph-factorization of symmetric complete bipartite multi-digraphs"Australasian J.Combinatorics. 20. 261-265 (1999)
[文献書誌] K.Ushio: "S_k-factorization of symmetric complete tripartite digraphs"Discrete Mathematics. 211. 281-286 (2000)
[文献書誌] A.Kaneko and M.Kano: "A straight-line embedding of two rooted trees in the plane"Discrete and Computational Geometry. 21. 603-613 (1999)
[文献書誌] A.Kaneko and M.Kano: "Balanced partitions of two sets of points in the plane"Computational Geometry:Theory and Applications. 13. 253-261 (1999)
[文献書誌] P.Frankl and N.Tokushige: "Erdos-Ko-Rado theorem for integer sequences"Combinatorica. 19. 55-63 (1999)
[文献書誌] A.Nakamoto: "Transformations in closed 2-cell embeddings on surfaces preserving specified properties"Discrete Mathematics. 197/198. 607-615 (1999)
[文献書誌] A.Nakamoto: "Generating quadrangulations of surfaces with minimum degree at least 3"J.Graph Theory. 30. 223-234 (1999)
[文献書誌] A.Nakamoto: "The YΔ-equivalence of kernels on the torus without taking duals"Yokohama Math.J.. 47. 183-190 (1999)
[文献書誌] B.Bollobas,O.Riordan,Z.Ryjacek,A.Saito and R.H.Schelp: "Closure and hamiltonian-connectivity of claw-free graphs"Discrete Mathematics. 195. 67-80 (1999)
[文献書誌] A.Saito: "Long paths,long cycles and their relative length"J.Graph Theory. 30. 91-99 (1999)
[文献書誌] a.Saito: "Degree sums ad graphs that are not covered by two cycles"J.Graph Theory. 32. 51-61 (1999)
[文献書誌] Z.Ryjacek,R.H.Schelp and A.Saito: "Closure,2-factors and cycle coverings in claw-free graphs"J.Graph Theory. 32. 109-117 (1999)

1999 年度 実績報告書

離散幾何における組合せ論的手法

研究代表者

斎藤 明 日本大学, 文理学部, 教授 (90186924)

研究成果

[文献書誌] H.Komuro,A.Nakamoto and S.Negami: "Diagonal flips in triangulations of closed surfaces with minimum degree at least 4"J.Combinatorial Theory,Ser.B. 76. 68-92 (1999)

[文献書誌] S.Lawrencenko and S.Negami: "Constructing the graphs that triangulate both the torus and the Klein bottle"J.Combinatorial Theory,Ser.B. 77. 211-218 (1999)

[文献書誌] S.Negami: "Diagonal flips of triangulations on surfaces,a survey"Yokohama Math.J.. 47. 1-40 (1999)

[文献書誌] S.Negami: "Note on frozen triangulations on closed surfaces"Yokohama Math.J.. 47. 191-202 (1999)

[文献書誌] T.Watanabe and S.Negami: "Diagonal flips in pseudo-triangulations of closed surfaces without loops"Yokohama Math.J.. 47. 213-223 (1999)

[文献書誌] R.Brunet,A.Nakamoto and S.Negami: "Every 5-connected triangulations of the Klein bottle is hamiltonian"Yokohama Math.J.. 47. 239-244 (1999)

[文献書誌] H.Imai,K.Sekine and K.Imai: "Computational investigations of all-terminal network reliability via BDDs"IEICE Trans.Fundamentals. E82-A. 714-721 (1999)

[文献書誌] 田島 玲,今井 浩: "三角形分割の最適性と整数計画による定式化"情報処理学会論文誌. 40. 2861-2871 (1999)

[文献書誌] H.Imai and M.Inaba: "Geometric clustering by divergence and its underlyingdiscrete proximity structures"IEICE Trans.Information and Systems. E83-D. 27-35 (2000)

[文献書誌] H.Maehara: "Lexell's theorem via an inscribed angle theorem"Amer.Math.Monthly. 106. 352-352 (1999)

[文献書誌] H.Maehara and A.Oshiro: "On Knotted necklaces of pearls"European J.Combinatorics. 20. 411-420 (1999)

[文献書誌] H.Maehara: "Geometry of frameworks"Yokohama Math.J.. 47. 41-65 (1999)

[文献書誌] H.Maehara: "Configuration spaces of pentagonal frameworks"European J.Combinatorics. 20. 839-844 (1999)

[文献書誌] H.Maehara and H.Noha: "Arranging solid balls on a table to make a k-component link"Ryukyu Math.J.. 12. 31-35 (1999)

[文献書誌] H.Enomoto and K.Ota: "Connected subgraphs with small degree sums in 3-connected planar graphs"J.Graph Theory. 30. 191-203 (1999)

[文献書誌] H.Enomoto,M.S,Miyauchi and K.Ota: "Lower bounds for the number of edge-crossings over the spine in a topological book embedding of a graph"Discrete Applied Mathematics. 92. 149-155 (1999)

[文献書誌] H.Enomoto and Y.Usami: "Extremal 2-connected graphs with given diameter"Tokyo J.Math.. 22. 1-16 (1999)

[文献書誌] H.Enomoto and M.S.Miyauchi: "Embedding graphs into a three page book with O(mlogn)crossings of edges over the spine"SIAM J.Discrete Mathematics. 12. 337-341 (1999)

[文献書誌] Y.Egawa and K.Ota: "Vertex-disjoint claws in graphs"Discrete Mathematics. 197/198. 225-246 (1999)

[文献書誌] K.Ushio: "S^^<^>_k-factorization of symmetric complete tripartite digraphs"Discrete Mathematics. 197/198. 791-797 (1999)

[文献書誌] K.Ushio: "Cycle-factorization of symmetric complete multipartite digraphs"Discrete Mathematics. 199. 273-278 (1999)

[文献書誌] K.Ushio: "Semi-evenly partite star-factorization of symmetric complete tripartite digraphs"Australasian J.Combinatorics. 20. 69-75 (1999)

[文献書誌] K.Ushio: "Bigraph-factorization of symmetric complete bipartite multi-digraphs"Australasian J.Combinatorics. 20. 261-265 (1999)

[文献書誌] K.Ushio: "S_k-factorization of symmetric complete tripartite digraphs"Discrete Mathematics. 211. 281-286 (2000)

[文献書誌] A.Kaneko and M.Kano: "A straight-line embedding of two rooted trees in the plane"Discrete and Computational Geometry. 21. 603-613 (1999)

[文献書誌] A.Kaneko and M.Kano: "Balanced partitions of two sets of points in the plane"Computational Geometry:Theory and Applications. 13. 253-261 (1999)

[文献書誌] P.Frankl and N.Tokushige: "Erdos-Ko-Rado theorem for integer sequences"Combinatorica. 19. 55-63 (1999)

[文献書誌] A.Nakamoto: "Transformations in closed 2-cell embeddings on surfaces preserving specified properties"Discrete Mathematics. 197/198. 607-615 (1999)

[文献書誌] A.Nakamoto: "Generating quadrangulations of surfaces with minimum degree at least 3"J.Graph Theory. 30. 223-234 (1999)

[文献書誌] A.Nakamoto: "The YΔ-equivalence of kernels on the torus without taking duals"Yokohama Math.J.. 47. 183-190 (1999)

[文献書誌] B.Bollobas,O.Riordan,Z.Ryjacek,A.Saito and R.H.Schelp: "Closure and hamiltonian-connectivity of claw-free graphs"Discrete Mathematics. 195. 67-80 (1999)

[文献書誌] A.Saito: "Long paths,long cycles and their relative length"J.Graph Theory. 30. 91-99 (1999)

[文献書誌] a.Saito: "Degree sums ad graphs that are not covered by two cycles"J.Graph Theory. 32. 51-61 (1999)

[文献書誌] Z.Ryjacek,R.H.Schelp and A.Saito: "Closure,2-factors and cycle coverings in claw-free graphs"J.Graph Theory. 32. 109-117 (1999)

1999 年度実績報告書

斎藤明日本大学, 文理学部, 教授 (90186924)

[文献書誌] 田島玲,今井浩: "三角形分割の最適性と整数計画による定式化"情報処理学会論文誌. 40. 2861-2871 (1999)