1996 Fiscal Year Annual Research Report

離散幾何の総合的研究

Research Project

Project/Area Number	08304019
Section	総合
Research Institution	University of the Ryukyus
Principal Investigator	前原濶琉球大学, 教育学部, 教授 (60044921)
Co-Investigator(Kenkyū-buntansha)	伊藤栄明統計数理研究所, 教授 (60000212) 榎本彦衛慶応大学, 理工学部, 教授 (00011669) 加納幹雄茨城大学, 工学部, 教授 (20099823) 小関道夫山形大学, 理学部, 教授 (90087073) 徳重典英琉球大学, 教育学部, 助教授 (00217481)
Keywords	格子点 / 整数距離グラフ / フレームワーク / 有理点 / 球面システム
Research Abstract	離散幾何の総合的研究で今年度得られた結果(の一部)の報告 1.任意の整数n>0に対して、ちょうどn個の格子点を通る円が存在する。(前原・松本による。スタインハウスの問題のバリエーションを解決したもの。) 2.どんな有限グラフGについても、その頂点集合を平面上に配置して、2頂点が隣接するときに限り、2頂点間の距離は整数になるようにすることができる。(前原・太田・徳重による。第1回カナダ計算幾何学会議(1989年)に提出された問題を解決したもの。) 3.X,Y(\|X\|≧3,\|Y\|≧5)を部集合とする平面上の完全2部グラフのフレームワークK(X,Y)は、Xが一直線上にあり、Yがそれと直交する直線上にある時に限って連続的に変形する。(前原・徳重による。どんな場合に無限小変形するかということについてはBolker-Rothにより既に知られていた。) 4.Nを大きい整数とし、XをN次元ユークリッド空間のn次元部分空間内の有理点の集合とする。n≧2ならXは2n+1次元ユークリッド空間の有理点のある集合と合同である。n≧3ならXは2n-1次元ユークリッド空間の有理点のある集合と相似である。(前原) 5.n次元空間内のn+2個の球面の集合は、その中のどのn+1個の球面も共通部分を持つが、n+2個全部の共通部分は空のとき、n次元の球面システムという。n=2のときは、円システムという。平面上では4個の単位円からなる円システムが存在する。n>2のとき単位球面からなるn次元の球面システムは存在しない。(前原・徳重) 今年度得られた他の研究結果については、研究成果報告書に含める予定。

Research Products

(24 results)

All Other

All Publications (24 results)

[Publications] H.Maehara: "On √Q-distances" European Journal of Combinatorics. 17. 271-277 (1996)
[Publications] H.Maehara: "A spatial unit-bar-framework which is rigid and triangle-free" Graphs and Combinatorics. 12. 341-344 (1996)
[Publications] P.Frankl: "Exponents of uniform L-systems" Journal of Conbinatorial Theory A. 75. 23-43 (1996)
[Publications] M.Ozeki: "On the notion of Jacobi polynomials for codes" Math.Proc.Camb.Philos.Soc.121. 15-30 (1997)
[Publications] M.Kano: "Edge-removing games of star type" Discrete Mathematics. 151. 113-119 (1996)
[Publications] H.Enomoto: "Connected spanning sabgraphs of 3-connected planar graphs" Journal of Combinatorial Theory B. 68. 314-323 (1996)
[Publications] H.Enomoto: "Graph decompositions without isolate vertices II" J.Math.Soc.Japan. 49. 161-180 (1997)
[Publications] K.Ota: "A degree condition for the existence of regular factors in K_<1,2>…" Journal of Graph Theory. 22. 59-64 (1996)
[Publications] Y.Egawa: "Vertex-disjoint cycles of the same length" J.Combin.Theory B. 66. 168-200 (1996)
[Publications] Y.Egawa: "Sufficient conditions for graphs to have (g,f)-factors" Discrete Mathematics. 151. 87-90 (1996)
[Publications] M.Urabe: "Topics on line segments and polygons" Discrete Mathematics. 51. 99-104 (1996)
[Publications] A.Kaneko: "A variation of the towers of Hanoi problem" Bull.Kurashiki Univ.Science and the Arts. 1. 65-71 (1996)
[Publications] T.Asano: "Variants for Hough transform for line detection" Computational Geometry : Theory and Applications. 6. 231-252 (1996)
[Publications] T.Asano: "Digital Halftoning Algorithms based on optimization criteria・・・" IEICE Trans.Fundamentals. E79-A(4). 524-532 (1996)
[Publications] Kouhei Asano: "An approximation algorithm for the Maximum independent set・・・" J.Combi.Math.& Combinatorial computing. 21. 33-39 (1996)
[Publications] M.Tsuchiya: "On double bound graphs whose complements are also double・・・" Proc.Schl.Sci.Tokai Univ.31. 13-17 (1996)
[Publications] M.Tsuchiya: "On Uniqueness of manifold posets and locally Cohen-Macauley." Southeast Asian Bulletin of Mathematics. 20. 13-17 (1996)
[Publications] M.Tanemura: "Kelvin polyhedra and analysis of crystallization" Forma. 11. 317-329 (1996)
[Publications] M.Tanemura: "On random packings by non-spherical particles" Acta Stereologica. 15. 97-102 (1996)
[Publications] Y.Itoh: "Addendum to Sfochastic Model of an Integrable Nonlinea System" J.Physical Society of Japan. 65. 4097-4097 (1996)
[Publications] K.Ando: "The bandwidth of a free with k-leaves is out most k/2" Discrete Mathematics. 150. 403-406 (1996)
[Publications] K.Ando: "A remark on the connectivity of the complement of a・・・" Discrete Mathematics. 151. 39-47 (1996)
[Publications] S.Nagami: "Polynomial invariants of graphs" Graphs and Combinatorics. 12. 189-198 (1996)
[Publications] R.Brunet: "Diagonal transformations of triangulations on closed surfaces・・・" J.Combin.Theory.B. 68. 295-309 (1996)

1996 Fiscal Year Annual Research Report

離散幾何の総合的研究

Principal Investigator

前原 濶 琉球大学, 教育学部, 教授 (60044921)

Research Products

[Publications] H.Maehara: "On √Q-distances" European Journal of Combinatorics. 17. 271-277 (1996)

[Publications] H.Maehara: "A spatial unit-bar-framework which is rigid and triangle-free" Graphs and Combinatorics. 12. 341-344 (1996)

[Publications] P.Frankl: "Exponents of uniform L-systems" Journal of Conbinatorial Theory A. 75. 23-43 (1996)

[Publications] M.Ozeki: "On the notion of Jacobi polynomials for codes" Math.Proc.Camb.Philos.Soc.121. 15-30 (1997)

[Publications] M.Kano: "Edge-removing games of star type" Discrete Mathematics. 151. 113-119 (1996)

[Publications] H.Enomoto: "Connected spanning sabgraphs of 3-connected planar graphs" Journal of Combinatorial Theory B. 68. 314-323 (1996)

[Publications] H.Enomoto: "Graph decompositions without isolate vertices II" J.Math.Soc.Japan. 49. 161-180 (1997)

[Publications] K.Ota: "A degree condition for the existence of regular factors in K_<1,2>…" Journal of Graph Theory. 22. 59-64 (1996)

[Publications] Y.Egawa: "Vertex-disjoint cycles of the same length" J.Combin.Theory B. 66. 168-200 (1996)

[Publications] Y.Egawa: "Sufficient conditions for graphs to have (g,f)-factors" Discrete Mathematics. 151. 87-90 (1996)

[Publications] M.Urabe: "Topics on line segments and polygons" Discrete Mathematics. 51. 99-104 (1996)

[Publications] A.Kaneko: "A variation of the towers of Hanoi problem" Bull.Kurashiki Univ.Science and the Arts. 1. 65-71 (1996)

[Publications] T.Asano: "Variants for Hough transform for line detection" Computational Geometry : Theory and Applications. 6. 231-252 (1996)

[Publications] T.Asano: "Digital Halftoning Algorithms based on optimization criteria・・・" IEICE Trans.Fundamentals. E79-A(4). 524-532 (1996)

[Publications] Kouhei Asano: "An approximation algorithm for the Maximum independent set・・・" J.Combi.Math.& Combinatorial computing. 21. 33-39 (1996)

[Publications] M.Tsuchiya: "On double bound graphs whose complements are also double・・・" Proc.Schl.Sci.Tokai Univ.31. 13-17 (1996)

[Publications] M.Tsuchiya: "On Uniqueness of manifold posets and locally Cohen-Macauley." Southeast Asian Bulletin of Mathematics. 20. 13-17 (1996)

[Publications] M.Tanemura: "Kelvin polyhedra and analysis of crystallization" Forma. 11. 317-329 (1996)

[Publications] M.Tanemura: "On random packings by non-spherical particles" Acta Stereologica. 15. 97-102 (1996)

[Publications] Y.Itoh: "Addendum to Sfochastic Model of an Integrable Nonlinea System" J.Physical Society of Japan. 65. 4097-4097 (1996)

[Publications] K.Ando: "The bandwidth of a free with k-leaves is out most k/2" Discrete Mathematics. 150. 403-406 (1996)

[Publications] K.Ando: "A remark on the connectivity of the complement of a・・・" Discrete Mathematics. 151. 39-47 (1996)

[Publications] S.Nagami: "Polynomial invariants of graphs" Graphs and Combinatorics. 12. 189-198 (1996)

[Publications] R.Brunet: "Diagonal transformations of triangulations on closed surfaces・・・" J.Combin.Theory.B. 68. 295-309 (1996)

前原濶琉球大学, 教育学部, 教授 (60044921)