1998 Fiscal Year Annual Research Report

グラフ論とその応用の研究

Research Project

Project/Area Number	09304020
Research Institution	The University of Electro-Communications
Principal Investigator	安藤清電気通信大学, 電気通信学部, 教授 (20096944)
Co-Investigator(Kenkyū-buntansha)	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)
Keywords	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
Research Abstract	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、夏季に電気通信大学で研究集会を開催し、成功させた。冬季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。以下に本研究の本年度における実績の概要を示す。k辺ワイド直径はそのグラフの直径のk次式のオーダーであること、またこの評価の多項式の次数は最良であることを示した(安藤、金子)。3次元空間内の互いに重なり合わない単位球15個によるtrefoil knotの構成、および、互いに重なり合わない、2種類の大きさの球12個によるtrefoil knotの構成を与えた。また、距離が2+√<2>離れた平行な2平面に挟まれる単位球の連鎖で結び目を作るには16個が必要であり、結び目がtrefoilの場合に限って16個で作れることを証明した。(前原)。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)。新しいvisibilityグラフを導入し、それを用いてMirzaianの予想への反例の構成に成功した(渡辺)。グラフの染色数に関するBrooksの定理を拡張した(岡村)。完全グラフの1-因子分解について旧来は計算機を用いて検証されていたところを、不変量の導入により識別する道を開いた(山崎)。グラフの直線埋め込み問題の中で2つの根付き木からなる林、各成分が星からなる林、等しい位数のn個の根付き木からなる林などが埋め込み可能であることを示し、同時に多項式時間アルゴリズムを与えた(加納、金子)。計算機何学の技法を適用することにより、画像の等高線表現を従来より10倍以上高速に求める方法を開発した(浅野)。ノード間の通信頻度が各ノードの重みの積に比例すると仮定した際に、木構造を持つ計算機ネットワークにおいて1つのリンクに故障が起こった時に、通信できなくなる確率を最小にする木構造のもつ性質を得た(神保)。臨界的な直径2のグラフの辺数の下限について「n【greater than or equal】23とし、Gを位数nの臨界的な直径2のグラフとすると、\|E(G)\|【greater than or equal】(5n-17)/2が成立する」という定理を得た(江川、安藤)。クラインの壼の既約三角形分割の完全な分類の完成した(根上)。クローフリーグラフにおけるハミルトンサイクルの存在条件及びRyjacek閉包と因子の関係を調べた(斉藤)。Upper Bound Graphは、グラフの観点からはEdge Clique Coverが、Posetの観点からはOrder Idealが、各々密接に関係していること示した(土屋)。頂点数が4k+6以上で最小次数k+2以上のグラフはk個のK_<1,3>を点素に含むことを示した(太田)。Oreの次数条件と閉路被覆に関するWang

Research Products

(32 results)

All Other

All Publications (32 results)

[Publications] K.Ando and H.Komuro: "The seven graphs whose H-transformations are uniquely determined" Ars Combin.46. 305-318 (1997)
[Publications] Y.Itoh and H.Maehara: "A variation to the ruin problem" Mathematica Japonica J.47. 97-102 (1998)
[Publications] H.Maehara: "A minimal rigid graph in the plane that is not constructible by ruler and compass" Yokohama Math.J.45. 109-112 (1998)
[Publications] H.Maehara and M.Matsumoto: "Is there a circle that passes through a given number of lattice points?" European J.Combinatorics. 19. 591-592 (1998)
[Publications] H.Maehara: "Embedding a set of rational points in lower dimensions" Discrete Math.192. 273-279 (1998)
[Publications] H.Enomoto,T.Nakamigawa and K.Ota: "On the pagenumber of complete bipartite graphs" J.Combinatorial Theory(Ser.B). 71. 111-120 (1997)
[Publications] H.Enomoto: "Toughness and the existence of κ-factors.III" Discrete Mathematics. 189. 277-282 (1998)
[Publications] H.Enomoto,M.Hagita and M.Matsumoto: "A note on difference sets" J.Combinatorial Theory(Ser.A). 84. 133-144 (1998)
[Publications] H.Enomoto,Y.Oda and K.Ota: "Pyramidal tours with step-backs and the asymmetric travelling salesman problem" Discrete Applied Mathematics. 87. 57-65 (1998)
[Publications] H.Enomoto,A.S.Llado,T.Nakamigawa and G.Ringel: "Super edge-magic graphs" SUT Journal of Mathematics. 34. 105-109 (1998)
[Publications] A.Kaneko and M.Watanabe: "String decompositions of Graphs" Ars Combinatoria. 49. 225-236 (1998)
[Publications] A.Kaneko and M.Watanabe: "A variation of The Towers of Hanoi Problem II" The Bulletin of Kurashiki University of Science and the Arts. 2. 49-51 (1997)
[Publications] S.Nakagawa and M.Watanabe: "On a valid path in a rectangle partotoned into horizontally aligned rectangle boxes" The Bulletin of Kurashiki University of Science and the Arts. 3. 57-64 (1998)
[Publications] S.Tazawa,Y.Jin and T.Shirakura: "Enumeration of labelled 2-connected Euler graphs" Journal of Combinatorics,Information & System Sciences. 23. 407-414 (1998)
[Publications] H.Okamura: "Six-terminal multicommodity flows in graphs" Memories of Konan University. 45. 105-114 (1998)
[Publications] Cai Maocheng,Li Yanjun,and M.Kano: "A[κ,κ+1]-factor containing given Hamiltonian cycle" Science in China(Series A). 41. 933-938 (1998)
[Publications] H.Enomoto,Y.Oda and K.Ota: "Pyramidal tours with step-backs and the asymmetric travelling salesman problem" Discrete Applied Mathematics. 87. 57-65 (1998)
[Publications] H.Enomoto,A.S.Llado,T.Nakamigawa and G.Ringel: "Super edge-magic graphs" SUT Journal of Mathematics. 34. 105-109 (1998)
[Publications] A.Kaneko and M.Watanabe: "String decompositions of Graphs" Ars Combinatoria. 49. 225-236 (1998)
[Publications] A.Kaneko and M.Watanabe: "A variation of The Towers of Hanoi Problem II" The Bulletin of Kurashiki University of Science and the Arts. 2. 49-51 (1997)
[Publications] S.Nakagawa and M.Watanabe: "On a valid path in a rectangle partotoned into horizontally aligned rectangle boxes" The Bulletin of Kurashiki University of Science and the Arts. 3. 57-64 (1998)
[Publications] S.Tazawa,Y.Jin and T.Shirakura: "Enumeration of labelled 2-connected Euler graphs" Journal of Combinatorics,Information & System Sciences. 23. 407-414 (1998)
[Publications] H.Okamura: "Six-terminal multicommodity flows in graphs" Memories of Konan University. 45. 105-114 (1998)
[Publications] Cai Maocheng,Li Yanjun,and M.Kano: "A[κ,κ+1]-factor containing given Hamiltonian cycle" Science in China(Series A). 41. 933-938 (1998)
[Publications] Y.Egawa: "Contractible cycles in graphs with girth at least 5" J.Combin.Theory(Ser.B). 74. 213-264 (1998)
[Publications] A.Kaneko: "On decomposition of triangle-free graphs under degree constraints" Journal of Graph Theory. 27. 7-9 (1998)
[Publications] S.Negami: "Ramsey-type theorems for spatial graphs and good drawings" J.Combin.Theory,(Ser.B). 72. 53-62 (1998)
[Publications] S.Negami: "Diagonal flips in triangulations of closed surfaces" Yokohama Math.J.45. 113-124 (1998)
[Publications] M.Tsuchiya: "On Uniform Intersection Numbers" Ars Combinatoria. 48. 225-232 (1998)
[Publications] P.Frankl,K.Ota and N.Tokushige: "Uniform intersecting families with covering number restrictions" Combinatorics,Probablity & Computing. 7. 47-56 (1998)
[Publications] T.Nishimura: "A new recursive theorem on n-extendibility" Graphs and Combinatorics. 13. 79-83 (1997)
[Publications] T.Iida and T.Nishimura: "Neighborhood conditions and κ-factors" Tokyo Journal of Mathematics. 20. 411-418 (1997)

1998 Fiscal Year Annual Research Report

グラフ論とその応用の研究

Principal Investigator

安藤 清 電気通信大学, 電気通信学部, 教授 (20096944)

Research Products

[Publications] K.Ando and H.Komuro: "The seven graphs whose H-transformations are uniquely determined" Ars Combin.46. 305-318 (1997)

[Publications] Y.Itoh and H.Maehara: "A variation to the ruin problem" Mathematica Japonica J.47. 97-102 (1998)

[Publications] H.Maehara: "A minimal rigid graph in the plane that is not constructible by ruler and compass" Yokohama Math.J.45. 109-112 (1998)

[Publications] H.Maehara and M.Matsumoto: "Is there a circle that passes through a given number of lattice points?" European J.Combinatorics. 19. 591-592 (1998)

[Publications] H.Maehara: "Embedding a set of rational points in lower dimensions" Discrete Math.192. 273-279 (1998)

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

[Publications] H.Enomoto: "Toughness and the existence of κ-factors.III" Discrete Mathematics. 189. 277-282 (1998)

[Publications] H.Enomoto,M.Hagita and M.Matsumoto: "A note on difference sets" J.Combinatorial Theory(Ser.A). 84. 133-144 (1998)

[Publications] H.Enomoto,Y.Oda and K.Ota: "Pyramidal tours with step-backs and the asymmetric travelling salesman problem" Discrete Applied Mathematics. 87. 57-65 (1998)

[Publications] H.Enomoto,A.S.Llado,T.Nakamigawa and G.Ringel: "Super edge-magic graphs" SUT Journal of Mathematics. 34. 105-109 (1998)

[Publications] A.Kaneko and M.Watanabe: "String decompositions of Graphs" Ars Combinatoria. 49. 225-236 (1998)

[Publications] A.Kaneko and M.Watanabe: "A variation of The Towers of Hanoi Problem II" The Bulletin of Kurashiki University of Science and the Arts. 2. 49-51 (1997)

[Publications] S.Nakagawa and M.Watanabe: "On a valid path in a rectangle partotoned into horizontally aligned rectangle boxes" The Bulletin of Kurashiki University of Science and the Arts. 3. 57-64 (1998)

[Publications] S.Tazawa,Y.Jin and T.Shirakura: "Enumeration of labelled 2-connected Euler graphs" Journal of Combinatorics,Information & System Sciences. 23. 407-414 (1998)

[Publications] H.Okamura: "Six-terminal multicommodity flows in graphs" Memories of Konan University. 45. 105-114 (1998)

[Publications] Cai Maocheng,Li Yanjun,and M.Kano: "A[κ,κ+1]-factor containing given Hamiltonian cycle" Science in China(Series A). 41. 933-938 (1998)

[Publications] H.Enomoto,Y.Oda and K.Ota: "Pyramidal tours with step-backs and the asymmetric travelling salesman problem" Discrete Applied Mathematics. 87. 57-65 (1998)

[Publications] H.Enomoto,A.S.Llado,T.Nakamigawa and G.Ringel: "Super edge-magic graphs" SUT Journal of Mathematics. 34. 105-109 (1998)

[Publications] A.Kaneko and M.Watanabe: "String decompositions of Graphs" Ars Combinatoria. 49. 225-236 (1998)

[Publications] A.Kaneko and M.Watanabe: "A variation of The Towers of Hanoi Problem II" The Bulletin of Kurashiki University of Science and the Arts. 2. 49-51 (1997)

[Publications] S.Nakagawa and M.Watanabe: "On a valid path in a rectangle partotoned into horizontally aligned rectangle boxes" The Bulletin of Kurashiki University of Science and the Arts. 3. 57-64 (1998)

[Publications] S.Tazawa,Y.Jin and T.Shirakura: "Enumeration of labelled 2-connected Euler graphs" Journal of Combinatorics,Information & System Sciences. 23. 407-414 (1998)

[Publications] H.Okamura: "Six-terminal multicommodity flows in graphs" Memories of Konan University. 45. 105-114 (1998)

[Publications] Cai Maocheng,Li Yanjun,and M.Kano: "A[κ,κ+1]-factor containing given Hamiltonian cycle" Science in China(Series A). 41. 933-938 (1998)

[Publications] Y.Egawa: "Contractible cycles in graphs with girth at least 5" J.Combin.Theory(Ser.B). 74. 213-264 (1998)

[Publications] A.Kaneko: "On decomposition of triangle-free graphs under degree constraints" Journal of Graph Theory. 27. 7-9 (1998)

[Publications] S.Negami: "Ramsey-type theorems for spatial graphs and good drawings" J.Combin.Theory,(Ser.B). 72. 53-62 (1998)

[Publications] S.Negami: "Diagonal flips in triangulations of closed surfaces" Yokohama Math.J.45. 113-124 (1998)

[Publications] M.Tsuchiya: "On Uniform Intersection Numbers" Ars Combinatoria. 48. 225-232 (1998)

[Publications] P.Frankl,K.Ota and N.Tokushige: "Uniform intersecting families with covering number restrictions" Combinatorics,Probablity & Computing. 7. 47-56 (1998)

[Publications] T.Nishimura: "A new recursive theorem on n-extendibility" Graphs and Combinatorics. 13. 79-83 (1997)

[Publications] T.Iida and T.Nishimura: "Neighborhood conditions and κ-factors" Tokyo Journal of Mathematics. 20. 411-418 (1997)

安藤清電気通信大学, 電気通信学部, 教授 (20096944)