1997 年度実績報告書

グラフ論とその応用の研究

研究課題

研究課題/領域番号	09304020
研究種目	基盤研究(A)
研究機関	電気通信大学
研究代表者	安藤清電気通信大学, 電気通信学部, 助教授 (20096944)
研究分担者	江川嘉美東京理科大学, 理学部, 教授 (70147502) 加納幹雄茨城大学, 工学部, 教授 (20099823) 渡辺守倉敷芸術大学, 産業科学技術学部, 教授 (90068916) 榎本彦衛慶応大学, 理工学部, 教授 (00011669) 前原濶琉球大学, 教育学部, 教授 (60044921)
キーワード	グラフ論 / 離散幾何 / 組み合せ幾何 / アルゴリズム / 計算幾何 / 組合せ論 / 位相幾何的グラフ論 / 離散最適化
研究概要	週一回の頻度で定期的に主要メンバーを中心にセミナーを行い、日常的に連絡を取りつつ研究をすすめた。また、夏には琉球大学でまた、冬には龍谷大学で他のグループと共同して研究集会を開催し、成功させた。本年度における成果としては、まず平面あるいは閉曲面に埋め込まれたグラフについての研究ではクラインの壺の既約三角形分割の完全な分類の完成し(根上)、平面上の点集合に2本の根付き木を直線埋め込みできることを示すことに成功し(金子、加納)、閉曲面の三角形分割あるいは四角形分割について、対角変形と呼ばれる基本操作でどの程度移り合えるかについて閉曲面の写像類群の構造を考察する手法を導入して研究成果をあげた(太田)。離散幾何学の分野では平面上に置かれた固い球の族に対して,これらの球を頂点集合とし,互いに接している球どうしは隣接しているとして得られるグラフについての研究し成果を得た(前原)。また、新しいvisibilityグラフを提案し、それを用いてMirzaianの予想への反例の構成に成功した(渡辺)。さらにグラフを用いて問題を定式化することにより、より効率的な新しい画像処理アルゴリズムを提案した(浅野)。グラフの部分グラフに分割する問題についてもいくつかの重要な結果を得た。部分グラフとしてstarを考え、与えられたサイズのstarが点素にk個存在するための、もとのグラフの最小次数条件について研究し、特に4点のstarK_<1.3>については、最小次数が2k以上の4k点のグラフは、唯一の例外を除き、k個の点素なK_<1.3>を含むことを示した(太田)。また、大きさが指定された部分グラフで孤立点をもたないものへ分割できるためのよい十分条件の発見にも成功した(榎本)。その他、Oreの次数条件と閉路被覆に関するWang予想を解決し(石上)、直径2の臨界グラフの辺数の精密な下界をえることに成功した(安藤、江川)。

研究成果

(27件)

すべてその他

すべて文献書誌 (27件)

[文献書誌] S.Negami and T.Tsukamoto: "Note on spatial graphs with good drawings" Proceedings of Knots96. 91-98 (1997)
[文献書誌] S.Lawrencenko and S.Negami: "Irreducible triangulations of the Klein bottle" J.Combin.Theory,Ser.B. 70. 265-291 (1997)
[文献書誌] A.Nakamoto, S.Negami and T.Tanuma: "Re-embedding structures of triangulations on closed surfaces" Sci.Rep.Yokohama Nat.Univ.,Sec.I. 44. 41-55 (1997)
[文献書誌] T.Roos, T.Asano, D.Ranjan, E.Welzl, and P.Widmayer: "Space Filling Curves and Their Use in the Design of Geometric Date Structures" Theoretical Computer Science. 181. 3-15 (1997)
[文献書誌] T.Asano, N.Katoh, T.Tokuyama, and H.Tmaki: "Covering Points in the plane by k-tours:towards a polynomial time approximation scheme for general k" Proc.29th ACM Symp.on THeory of Computing. 275-283 (1997)
[文献書誌] H.Maehara, K.Ota, N.Tokushige: "Every graph is an integral distance graph" J.Combin.Theory(A). 80. 290-294 (1997)
[文献書誌] H.Maehara, H.Noha: "On the graph represented by a family of solid balls on a table" Ryukyu Math.J.10. 51-64 (1997)
[文献書誌] Y.Itoh, H.Maehara: "A variation to the ruin problem" Mathematica Japonica. 47. 97-102 (1998)
[文献書誌] Enomoto,H. and Matsunaga,S: "Graph decompositions without isolated vertices.II" J.Math.Soc.Japan. Vol.49. 161-181 (1997)
[文献書誌] Enomoto,H. and Matsunaga,S: "Graph decompositions without isolated vertices.III" Journal of Graph Theory. Vol.24. 155-164 (1997)
[文献書誌] Enomoto,H., Ota,K. and Hirohata,K: "Long cycles passing through a specified edge in a 3-connected graph" Journal of Graph Theory. Vol.24. 275-279 (1997)
[文献書誌] Enomoto,H., Nakamigawa,T. and Ota,K: "On the pagenumber of complete bipartite graphs" Journal of Combinatorial Theory(Ser.B). Vol.71. 111-120 (1997)
[文献書誌] A.Kaneko, M-M.Watanabe: "A Variation of,Towers of Hanoi Problem II" Bull.of Kurashiki Univ.of Science and the Arts. Vol.2. 49-51 (1997)
[文献書誌] A.KAneko: "On decomposition of triangle-free graphs under degree constraints" Journal of Graph Theory. Vol27,No.1. 7-9 (1998)
[文献書誌] Atsuhiro Nakamoto and Katsuhiro Ota: "Diagonal Transformations in Quadrangulations and Dehn Twists Preserving Cycle Parities" Journal of Combinatorial Theory Series B. Vol69,No2. 125-141 (1997)
[文献書誌] Atsuhiro Nakamoto,Katsuhiro Ota and Takayuki Tanuma: "Three-Cycle Reversions in Oriented Planar Triangulations" Yokohama Mathematical Journal. Vol44,No2. 123-128 (1997)
[文献書誌] Atsuhiro Nakamoto and Katsuhiro Ota: "Diagonal Transformations of Graphs and Dehn Twists of Surfaces" Journal of Combinatorial Theory Series B. Vol70,No2. 292-300 (1997)
[文献書誌] M.Tsutiya and H.Era: "Remarks on Relations between Upper Bound Graphs and Double Bound Graphs" Proceedings of the School of Science,Tokai Univ.32. 1-6 (1997)
[文献書誌] M.Tsutiya and H.Era: "On Upper Bound Graphs whose Complements are also Upper Bound Graphs" Discrete Mathematics. 179. 103-109 (1998)
[文献書誌] Y.Ishigami and S.Tani: "VC-dimensions of finite automata and commutative finite automata with k alphabets and n states" Discrete Applied Mathematics. Vol.74. 123-134 (1997)
[文献書誌] M.Kano: "A straight-line embedding of two or more rooted trees in the plane" Proceedings of The ninth Canadian Conference on Computational Geometry. 50-55 (1997)
[文献書誌] Y.Egawa, M.Kano and A.Kelmans: "Star partitions of graphs" J.of Graph Theory. Vol.25. 185-190 (1997)
[文献書誌] K.Ando, and Y.Egawa: "The minmum number of edges in a vertex diameter-2-critical graph" Discrete Math.167/168. 35-63 (1997)
[文献書誌] Y.Egawa: "Contractible cycles in graphs with large minimum degree" Discrete Math.171. 103-119 (1997)
[文献書誌] Y.Egawa: "Graph labellings in elementaly abelian 2-groups" Tokyo J.Math.20. 365-379 (1997)
[文献書誌] A.Tamura: "The generalized stable set problem for perfect bidirected graphs" Journal of the Operations Research Society of Japan. 40. 401-414 (1997)
[文献書誌] K.Ando, and H.Komuro: "The seven graphs which have unique H-transformation" Ars Combinatoria. 46. 305-318 (1997)

1997 年度 実績報告書

グラフ論とその応用の研究

研究代表者

安藤 清 電気通信大学, 電気通信学部, 助教授 (20096944)

研究成果

[文献書誌] S.Negami and T.Tsukamoto: "Note on spatial graphs with good drawings" Proceedings of Knots96. 91-98 (1997)

[文献書誌] S.Lawrencenko and S.Negami: "Irreducible triangulations of the Klein bottle" J.Combin.Theory,Ser.B. 70. 265-291 (1997)

[文献書誌] A.Nakamoto, S.Negami and T.Tanuma: "Re-embedding structures of triangulations on closed surfaces" Sci.Rep.Yokohama Nat.Univ.,Sec.I. 44. 41-55 (1997)

[文献書誌] T.Roos, T.Asano, D.Ranjan, E.Welzl, and P.Widmayer: "Space Filling Curves and Their Use in the Design of Geometric Date Structures" Theoretical Computer Science. 181. 3-15 (1997)

[文献書誌] T.Asano, N.Katoh, T.Tokuyama, and H.Tmaki: "Covering Points in the plane by k-tours:towards a polynomial time approximation scheme for general k" Proc.29th ACM Symp.on THeory of Computing. 275-283 (1997)

[文献書誌] H.Maehara, K.Ota, N.Tokushige: "Every graph is an integral distance graph" J.Combin.Theory(A). 80. 290-294 (1997)

[文献書誌] H.Maehara, H.Noha: "On the graph represented by a family of solid balls on a table" Ryukyu Math.J.10. 51-64 (1997)

[文献書誌] Y.Itoh, H.Maehara: "A variation to the ruin problem" Mathematica Japonica. 47. 97-102 (1998)

[文献書誌] Enomoto,H. and Matsunaga,S: "Graph decompositions without isolated vertices.II" J.Math.Soc.Japan. Vol.49. 161-181 (1997)

[文献書誌] Enomoto,H. and Matsunaga,S: "Graph decompositions without isolated vertices.III" Journal of Graph Theory. Vol.24. 155-164 (1997)

[文献書誌] Enomoto,H., Ota,K. and Hirohata,K: "Long cycles passing through a specified edge in a 3-connected graph" Journal of Graph Theory. Vol.24. 275-279 (1997)

[文献書誌] Enomoto,H., Nakamigawa,T. and Ota,K: "On the pagenumber of complete bipartite graphs" Journal of Combinatorial Theory(Ser.B). Vol.71. 111-120 (1997)

[文献書誌] A.Kaneko, M-M.Watanabe: "A Variation of,Towers of Hanoi Problem II" Bull.of Kurashiki Univ.of Science and the Arts. Vol.2. 49-51 (1997)

[文献書誌] A.KAneko: "On decomposition of triangle-free graphs under degree constraints" Journal of Graph Theory. Vol27,No.1. 7-9 (1998)

[文献書誌] Atsuhiro Nakamoto and Katsuhiro Ota: "Diagonal Transformations in Quadrangulations and Dehn Twists Preserving Cycle Parities" Journal of Combinatorial Theory Series B. Vol69,No2. 125-141 (1997)

[文献書誌] Atsuhiro Nakamoto,Katsuhiro Ota and Takayuki Tanuma: "Three-Cycle Reversions in Oriented Planar Triangulations" Yokohama Mathematical Journal. Vol44,No2. 123-128 (1997)

[文献書誌] Atsuhiro Nakamoto and Katsuhiro Ota: "Diagonal Transformations of Graphs and Dehn Twists of Surfaces" Journal of Combinatorial Theory Series B. Vol70,No2. 292-300 (1997)

[文献書誌] M.Tsutiya and H.Era: "Remarks on Relations between Upper Bound Graphs and Double Bound Graphs" Proceedings of the School of Science,Tokai Univ.32. 1-6 (1997)

[文献書誌] M.Tsutiya and H.Era: "On Upper Bound Graphs whose Complements are also Upper Bound Graphs" Discrete Mathematics. 179. 103-109 (1998)

[文献書誌] Y.Ishigami and S.Tani: "VC-dimensions of finite automata and commutative finite automata with k alphabets and n states" Discrete Applied Mathematics. Vol.74. 123-134 (1997)

[文献書誌] M.Kano: "A straight-line embedding of two or more rooted trees in the plane" Proceedings of The ninth Canadian Conference on Computational Geometry. 50-55 (1997)

[文献書誌] Y.Egawa, M.Kano and A.Kelmans: "Star partitions of graphs" J.of Graph Theory. Vol.25. 185-190 (1997)

[文献書誌] K.Ando, and Y.Egawa: "The minmum number of edges in a vertex diameter-2-critical graph" Discrete Math.167/168. 35-63 (1997)

[文献書誌] Y.Egawa: "Contractible cycles in graphs with large minimum degree" Discrete Math.171. 103-119 (1997)

[文献書誌] Y.Egawa: "Graph labellings in elementaly abelian 2-groups" Tokyo J.Math.20. 365-379 (1997)

[文献書誌] A.Tamura: "The generalized stable set problem for perfect bidirected graphs" Journal of the Operations Research Society of Japan. 40. 401-414 (1997)

[文献書誌] K.Ando, and H.Komuro: "The seven graphs which have unique H-transformation" Ars Combinatoria. 46. 305-318 (1997)

1997 年度実績報告書

安藤清電気通信大学, 電気通信学部, 助教授 (20096944)