Organizational study toward the final solution to Planar Cover Conjecture

• Project/Area Number: 17340025
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Yokohama National University
• Principal Investigator: NEGAMI Seiya Yokohama National University, 教育人間科学部, 教授 (40164652)
• Co-Investigator(Kenkyū-buntansha): NAKAMOTO Atsuhiro 横浜国立大学, 教育人間科学部, 準教授 (20314445) ; YAMAMOTO Ko 横浜国立大学, 教育人間科学部, 講師 (00293168) ; OTA Katsuhiro 慶応義塾大学, 理工学部, 教授 (40213722) ; SATO Iwao 小山工業高等専門学校, 一般科目, 教授 (70154036)
• Project Period (FY): 2005 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥14,710,000 (Direct Cost: ¥12,700,000、Indirect Cost: ¥2,010,000); Fiscal Year 2008: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000); Fiscal Year 2007: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000); Fiscal Year 2006: ¥2,600,000 (Direct Cost: ¥2,600,000); Fiscal Year 2005: ¥3,400,000 (Direct Cost: ¥3,400,000)
• Keywords: 離散数学 / トポロジー / 位相幾何学的グラフ理論 / 平面被覆予想 / グラフの被覆 / グラフの平面性 / 射影平面的グラフ / 閉曲面の三角形分割

Research Abstract

位相幾何学的グラフ理論における未解決問題の1つである「平面被覆予想」の最終的な解決を目指して組織的に研究を行った。予想の解決には至らなかったが、平面上の六角形分割に対する放電法を利用するという証明手法が提案された。また、予想の解決と関連して、閉曲面上の三角形分割の弛緩度や識別数と再埋蔵理論、グラフの被覆の代数的な数え上げ理論など、位相幾何学的グラフ理論における様々なテーマについて多くの定理を得た。

Research Products

• [Journal Article] K_6-Minors in triangulations on the Klein bottle (2008)
  • Author(s): Ken-ichi Kawarabayashi, Raiji Mukae and Atsuhiro Nakamoto
  • Journal Title: SIAM J. Discrete Math no.1 Pages: 96-108
  • Peer Reviewed
• [Journal Article] 3-Connected planar graphs are 2-distinguishable with few exceptions (2008)
  • Author(s): Tomotaka Fukuda, Seiya Negami and Thomas W. Tucker
  • Journal Title: Yokohama Math. J. 54 no.2 Pages: 143-153
  • Peer Reviewed
• [Journal Article] N-Flips in even triangulations on the projective plane (2008)
  • Author(s): Atsuhiro Nakamoto and Yusuke Suzuki
  • Journal Title: Discrete Math. 308 no.23 Pages: 5454-5462
  • Peer Reviewed
• [Journal Article] Geometric realization of a triangulation on the projective plane with one face removed (2008)
  • Author(s): C. Paul Bonnington and Atsuhiro Nakamoto
  • Journal Title: Discrete Comput. Geom. 40 no.1 Pages: 141-157
  • Peer Reviewed
• [Journal Article] 5-Chromatic even triangulations on surfaces (2008)
  • Author(s): Atsuhiro Nakamoto
  • Journal Title: Discrete Math. 308 no.12 Pages: 2571-2580
  • Peer Reviewed
• [Journal Article] Bartholdi zeta functions of periodic simple graphs (2008)
  • Author(s): Iwao Sato
  • Journal Title: Far East J. Math. Sci. (FJMS)30 no.2 Pages: 233-251
  • Peer Reviewed
• [Journal Article] Spectra of Laplacian matrices of semiregular bipartite graphs (2008)
  • Author(s): Iwao Sato
  • Journal Title: Far East J. Math. Sci. (FJMS)30 no.3 Pages: 557-566
  • Peer Reviewed
• [Journal Article] The stochastic weighted complexity of a group covering of a digraph (2008)
  • Author(s): Iwao Sato
  • Journal Title: Linear Algebra Appl. 429 no.8-9 Pages: 1905-1914
  • Peer Reviewed
• [Journal Article] Weighted Bartholdi zeta functions of graph coverings (2008)
  • Author(s): Iwao Sato
  • Journal Title: Discrete Math. 308 no.12 Pages: 2600-2606
  • Peer Reviewed
• [Journal Article] Distinguishing numbers and re-embedding structures of triangulations on closed surfaces (2008)
  • Author(s): Seiya Negami
  • Journal Title: Electronic Nates in Discrete Mathematics 31 Pages: 227-230
  • Peer Reviewed
• [Journal Article] 3-Connected planar graphs are 2-distinguishable (2008)
  • Author(s): Tomotaka Fukuda
  • Journal Title: Yokohama Mathematical Journal 54 Pages: 143-153
  • Peer Reviewed
• [Journal Article] The distinguishing numbers of triangulations on the projective plane. Proceedings of the 38th Southeastern International Conference on Combinatorics, Graph Theory and Computing (2007)
  • Author(s): Seiya Negami
  • Journal Title: Congr. Numer. 186 Pages: 135-144
  • Peer Reviewed
• [Journal Article] K_6-Minors in triangu-lations on the double torus. Proceedings of the 38th Southeastern International Conference on Combinatorics, Graph Theory and Computings (2007)
  • Author(s): Atsuhiro NakamotoAtsuhiro Nakamoto, Yoshiaki Oda and Katsuhiro Ota
  • Journal Title: Congr. Numer. 188 Pages: 150-160
  • Peer Reviewed
• [Journal Article] 3-Colorable even embeddings on closed surfaces (2007)
  • Author(s): Atsuhiro Nakamoto and Norihito Sasanuma
  • Journal Title: Graphs Combin. 23 no.1 Pages: 87-95
  • Peer Reviewed
• [Journal Article] The Erdos-Posa property for vertex-and edge-disjoint odd cycles in graphs on orientable surfaces (2007)
  • Author(s): Ken-ichi Kawarabayashi and Atsuhiro Nakamoto
  • Journal Title: Discrete Math. 307 no.6 Pages: 764-768
  • Peer Reviewed
• [Journal Article] A new Bartholdi zeta function of a graph (2007)
  • Author(s): Iwao Sato
  • Journal Title: Int. J. Algebra 1 no.5-8 Pages: 269-281
  • Peer Reviewed
• [Journal Article] Bartholdi zeta and L-functions of weighted digraphs, their coverings and products (2007)
  • Author(s): Young-Bin Choe, Jin Ho Kwak, Yong Sung Park and Iwao Sato
  • Journal Title: Adv.Math. 213 no.2 Pages: 865-886
  • Peer Reviewed
• [Journal Article] Iwao Sato and Yaokun Wu, Homomorphisms, representations and characteristic polynomials of digraphs (2007)
  • Author(s): Aiping Deng
  • Journal Title: Linear Algebra Appl. 423 no.2-3 Pages: 386-407
  • Peer Reviewed
• [Journal Article] Iwao Sato and Yaokun Wu, Characteristic polynomials of ramified uniform covering digraphs (2007)
  • Author(s): Aiping Deng
  • Journal Title: European J.Combin. 28 no.4 Pages: 1099-1114
  • Peer Reviewed
• [Journal Article] Bartholdi zeta functions for hypergraphs (2007)
  • Author(s): Iwao Sato
  • Journal Title: Electron. J. Combin. 14 no.1, Note 2, 9 pp.(electronic)
  • Peer Reviewed
• [Journal Article] Zeta functions and complexities of a semiregular bipartite graph and its line graph (2007)
  • Author(s): Iwao Sato
  • Journal Title: Discrete Math. 307 no.2 Pages: 237-245
  • Peer Reviewed
• [Journal Article] Yong Sung Park and Iwao Sato, Weighted complexities of graph products and bundles (2007)
  • Author(s): Jin Ho Kwak
  • Journal Title: European J. Combin. 28 no.1 Pages: 228-245
  • Peer Reviewed
• [Journal Article] The distinguishing number of triangulations on the projective plane (2007)
  • Author(s): S. Negami
  • Journal Title: Congressus Numernatium 186 Pages: 135-144
  • Peer Reviewed
• [Journal Article] 3-colorable even embeddings on closed surfaces (2007)
  • Author(s): A. Nakamoto
  • Journal Title: Graphs and Combinatorics 23 Pages: 87-95
  • Peer Reviewed
• [Journal Article] A new Bartholdi zeta function of a graph (2007)
  • Author(s): I. Sato
  • Journal Title: Int. J. Algebra 1 Pages: 269-281
  • Peer Reviewed
• [Journal Article] Kiyoshi Ando and Atsuhiro Nakamoto, Tight quadrangu-lations on the sphere (2006)
  • Author(s): Hideo Komuro
  • Journal Title: Discrete Math. 306 no.2 Pages: 278-283
  • Peer Reviewed
• [Journal Article] Tadashi Sakuma and Yusuke Suzuki, N-Flips in even triangulations on the sphere (2006)
  • Author(s): Atsuhiro Nakamoto
  • Journal Title: J. Graph Theory 51 no.3 Pages: 260-268
  • Peer Reviewed
• [Journal Article] Weighted Ramsey problem. Australas (2006)
  • Author(s): Jun Fujisawa and Katsuhiro Ota
  • Journal Title: J. Combin 34 Pages: 331-342
  • Peer Reviewed
• [Journal Article] Weighted zeta functions of graph coverings (2006)
  • Author(s): Iwao Sato
  • Journal Title: Electron. J. Combin. 13(Research Paper 91, 12 pp.(electronic))no.1
  • Peer Reviewed
• [Journal Article] Coverings of digraphs (2006)
  • Author(s): Iwao Sato
  • Journal Title: Far East J. Math. Sci. (FJMS)23 no.3 Pages: 281-293
  • Peer Reviewed
• [Journal Article] Edge zeta functions of graph coverings (2006)
  • Author(s): Iwao Sato
  • Journal Title: Ars Combin 81 Pages: 225-233
  • Peer Reviewed
• [Journal Article] Spectra of line graphs of semiregular bipartite graphs (2006)
  • Author(s): Iwao Sato
  • Journal Title: Far East J. Math. Sci. (FJMS)23 no.1 Pages: 137-144
  • Peer Reviewed
• [Journal Article] Zeta functions of line, middle, total graphs of a graph and their coverings (2006)
  • Author(s): Jin Ho Kwak and Iwao Sato
  • Journal Title: Linear Algebra Appl. 418 no.1 Pages: 234-256
  • Peer Reviewed
• [Journal Article] L-functions for line graphs of semiregular bipartite graphs (2006)
  • Author(s): Iwao Sato
  • Journal Title: Linear Algebra Appl. 416 no.2-3 Pages: 373-388
  • Peer Reviewed
• [Journal Article] Isomorphisms of connected cyclic abelian covers of symmetric digraphs (2006)
  • Author(s): Iwao Sato and Jauen Lee
  • Journal Title: Ars Combin 80 Pages: 129-139
  • Peer Reviewed
• [Journal Article] Weighted Bartholdi zeta functions of graphs (2006)
  • Author(s): Iwao Sato
  • Journal Title: European J. Combin. 27 no.5 Pages: 644-657
  • Peer Reviewed
• [Journal Article] A pair of forbidden subgraphs and perfect matchings (2006)
  • Author(s): S.Fujita
  • Journal Title: J. Combin. Theory Ser. B 96 Pages: 315-324
• [Journal Article] Weighted Ramsey problem (2006)
  • Author(s): J.fujisawa
  • Journal Title: Australas, J. combin. 34 Pages: 33132-33132
• [Journal Article] Tight quadrangulations on the sphere (2006)
  • Author(s): H.Komuro
  • Journal Title: Discrete Math. 306 Pages: 278-283
• [Journal Article] N-flips in even traingulations on the sphere (2006)
  • Author(s): A.Nakamoto
  • Journal Title: J. Graph Theory 513 Pages: 260-268
• [Journal Article] Coverings of digraphs (2006)
  • Author(s): I.Sato
  • Journal Title: Far East J. Math. Sci. 23 Pages: 281-293
• [Journal Article] Edge zeta functions of graph coverings (2006)
  • Author(s): I.Sato
  • Journal Title: Ars Combin. 81 Pages: 225-233
• [Journal Article] Looseness ranges of triangulations on closed surfaces (2005)
  • Author(s): Seiya Negami
  • Journal Title: Discrete Math. 303 no.1-3 Pages: 167-174
  • Peer Reviewed
• [Journal Article] Projective-planar double coverings of graphs (2005)
  • Author(s): Seiya Negami
  • Journal Title: European J. Combin. 26 no.3-4 Pages: 325-338
  • Peer Reviewed
• [Journal Article] 5-Chromatic even triangulations on the Klein bottle (2005)
  • Author(s): Atsuhiro Nakamoto
  • Journal Title: Discrete Math. 303 no.1-3 Pages: 154-166
  • Peer Reviewed
• [Journal Article] Diagonal flips in Hamiltonian triangulations on the projective plane (2005)
  • Author(s): Ryuichi Mori and Atsuhiro Nakamoto
  • Journal Title: Discrete Math. 303 no.1-3 Pages: 142-153
  • Peer Reviewed
• [Journal Article] Acute triangles in triangulations on the plane with minimum degree at least 4 (2005)
  • Author(s): Kenji Koyama and Atsuhiro Nakamoto
  • Journal Title: Discrete Math. 303 no.1-3 Pages: 104-116
  • Peer Reviewed
• [Journal Article] On 3-coloring of plane triangulations (2005)
  • Author(s): Atsuhiro Nakamoto, Katsuhiro Ota and Mamoru Watanabe
  • Journal Title: Ars Combin 75 Pages: 157-162
  • Peer Reviewed
• [Journal Article] Acute triangles in 4-connected maximal plane graphs (2005)
  • Author(s): Ken-ichi Kawarabayashi, Atsuhiro Nakamoto, Yoshiaki Oda and Mamoru Watanabe
  • Journal Title: Discrete Math. 292 no.1-3 Pages: 95-106
  • Peer Reviewed
• [Journal Article] Bartholdi zeta functions of group coverings of digraphs (2005)
  • Author(s): Iwao Sato
  • Journal Title: Far East J. Math. Sci.(FJMS)18 no.3 Pages: 321-339
  • Peer Reviewed
• [Journal Article] Lifts of automorphisms of symmetric digraphs associated with cyclic abelian covers (2005)
  • Author(s): Iwao Sato
  • Journal Title: III.J.Combin. Math. Combin. Comput 52 Pages: 3-16
  • Peer Reviewed
• [Journal Article] Diagonal flips in Hamiltonian triangulations on the projective plane (2005)
  • Author(s): R.Mori
  • Journal Title: Discrete Math. 303 Pages: 142-153
• [Journal Article] 5-Chromatic even triangulations on the Klein bottle (2005)
  • Author(s): A.Nakamoto
  • Journal Title: Discrete Math. 303 Pages: 154-166
• [Journal Article] On 3-coloring of plane triangulations (2005)
  • Author(s): A.Nakamoto
  • Journal Title: Ars Combin. 75 Pages: 157-162
• [Journal Article] Looseness ranges of triangulations on closed surfaces (2005)
  • Author(s): S.Negami
  • Journal Title: Discrete Math. 303 Pages: 167-174
• [Journal Article] Projective-planar double coverings of graphs (2005)
  • Author(s): S.Negami
  • Journal Title: European J.Combin. 26 Pages: 325-338
• [Journal Article] Lifts of automorphisms of symmetric digraphs associated with cyclic abelian covers.III, (2005)
  • Author(s): I.Sato
  • Journal Title: J.Combin.Math.Combin.Comput. 52 Pages: 3-16
• [Presentation] Forests in graphs (2008)
  • Author(s): Katsuhiro Ota
  • Organizer: The 20th Workshop on Topological Graph Theory in Yokohama
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2008-11-28
• [Presentation] Bartholdi zeta functions of hyper graphs (2008)
  • Author(s): Iwao Sato
  • Organizer: The 20th Workshop on Topological Graph Theory in Yokohama
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2008-11-26
• [Presentation] Distinguishing number and re-embedding of graphs on surfaces (2008)
  • Author(s): Seiya Negami
  • Organizer: The 20th Workshop on Topological Graph Theory in Yokohama
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2008-11-26
• [Presentation] Domatic number of triangulations on surfaces (2008)
  • Author(s): Atsuhiro Nakamoto
  • Organizer: The 20th Workshop on Topological Graph Theory in Yokohama
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2008-11-25
• [Presentation] The distinguishing number of 4-regular quadrangulations on the Klein bottle (2008)
  • Author(s): Ko Yamamoto
  • Organizer: The 20th Workshop on Topological Graph Theory in Yokohama
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2008-11-25
• [Presentation] どうやって平面被覆予想を解決するか (2007)
  • Author(s): 根上生也
  • Organizer: 第19回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2007-11-16
• [Presentation] 球面上のn角形分割について (2007)
  • Author(s): 山本 光
  • Organizer: 第19回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2007-11-16
• [Presentation] Weighted Bartholdi zeta functions of graphs (2007)
  • Author(s): 佐藤巌
  • Organizer: 第19回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2007-11-15
• [Presentation] トーラスの偶角形分割のN-変形とDehn twist (2007)
  • Author(s): 中本敦浩
  • Organizer: 第19回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2007-11-15
• [Presentation] Star coloring of cubic graphs (2007)
  • Author(s): 太田克弘
  • Organizer: 離散数学とその応用研究集会2007
  • Place of Presentation: 下呂市民会館
  • Year and Date: 2007-08-08
• [Presentation] どうやって平面被覆予想を解けばよいのか (2007)
  • Author(s): 根上生也
  • Organizer: 離散数学とその応用研究集会2007
  • Place of Presentation: 下呂市民会館
  • Year and Date: 2007-08-08
• [Presentation] Bartholdi zeta functions of some graphs (2007)
  • Author(s): 佐藤 巌
  • Organizer: 離散数学とその応用研究集会2007
  • Place of Presentation: 下呂市民会館
  • Year and Date: 2007-08-07
• [Presentation] 閉曲面上の全着色された三角形分割の対角変形 (2007)
  • Author(s): 山本 光
  • Organizer: 離散数学とその応用研究集会2007
  • Place of Presentation: 下呂市民会館
  • Year and Date: 2007-08-07
• [Presentation] K6-Minors in triangulations on the double torus (2007)
  • Author(s): 中本敦浩
  • Organizer: 離散数学とその応用研究集会2007
  • Place of Presentation: 下呂市民会館
  • Year and Date: 2007-08-07
• [Presentation] Around planar cover conjecture, International Workshop on Combinatorics 2007 (2007)
  • Author(s): Seiya Negami
  • Organizer: The 21st Century COE Program at Keio, Integrative Mathematical Sciences
  • Place of Presentation: 慶応義塾大学
  • Year and Date: 2007-06-07
• [Presentation] The distinguishing number of triangulations on the projective plane (2007)
  • Author(s): Seiya Negami
  • Organizer: 38th Southeastern International Conference on Combinatorics, Graph Theory, and Computing
  • Place of Presentation: アメリカ合衆国, フロリダ
  • Year and Date: 2007-03-09
• [Presentation] K6-Minors in triangulations on surfaces (2007)
  • Author(s): Atsuhiro Nakamoto
  • Organizer: 38th Southeastern International Conference on Combinatorics, Graph Theory, and Computing
  • Place of Presentation: アメリカ合衆国, フロリダ
  • Year and Date: 2007-03-09
• [Presentation] Toughness and bipartite-minors in graphs (2007)
  • Author(s): Katsuhiro Ota
  • Organizer: 38th Southeastern International Conference on Combinatorics, Graph Theory, and Computing
  • Place of Presentation: アメリカ合衆国, フロリダ
  • Year and Date: 2007-03-09
• [Presentation] Recognizable colorings of paths and cycles (2006)
  • Author(s): 太田克弘
  • Organizer: 第18回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2006-11-17
• [Presentation] Chromatic number of even triangulations on the Klein bottle (2006)
  • Author(s): 中本敦浩
  • Organizer: 第18回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2006-11-17
• [Presentation] 閉曲面上のグラフの識別可能性 (2006)
  • Author(s): 根上生也
  • Organizer: 第18回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2006-11-16
• [Presentation] 球面上の五角形分割 (2006)
  • Author(s): 山本光
  • Organizer: 第18回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2006-11-16
• [Presentation] Geometric reali-zation of 5-connected triangu lations of the Mobius band (2006)
  • Author(s): Atsuhiro Nakamoto
  • Organizer: International Workshop on Discrete Mathematics and its Applications
  • Place of Presentation: 茨城大学
  • Year and Date: 2006-08-03
• [Presentation] 3-Connected planar graphs are 2-distinguishable with few exceptions (2006)
  • Author(s): Seiya Negami
  • Organizer: International Workshop on Discrete Mathematics and its Applications
  • Place of Presentation: 茨城大学
  • Year and Date: 2006-08-02
• [Presentation] Bartholdi zeta functions of group coverings of digraphs (2006)
  • Author(s): Iwao Sato
  • Organizer: International Workshop on Discrete Mathematics and its Applications
  • Place of Presentation: 茨城大学
  • Year and Date: 2006-08-02
• [Presentation] Toughness of K_<a,t>-minors-free graphs (2006)
  • Author(s): Katsuhiro Ota
  • Organizer: International Workshop on Discrete Mathematics and its Applications
  • Place of Presentation: 茨城大学
  • Year and Date: 2006-08-01
• [Presentation] The distinguishing number of graphs embedded on surfaces (2006)
  • Author(s): Seiya Negami
  • Organizer: SIAM Conference on Discrete Mathematics
  • Place of Presentation: University of Victoriaカナダ, ビクトリア
  • Year and Date: 2006-06-26
• [Presentation] Chromatic even triangulations on surfaces (2006)
  • Author(s): Atsuhiro Nakamoto
  • Organizer: SIAM Conference on Discrete Mathematics
  • Place of Presentation: University of Victoriaカナダ, ビクトリア
  • Year and Date: 2006-06-26
• [Presentation] Looseness and re-embedding structures of triangu-lations on closed surfaces (2005)
  • Author(s): Seiya Negami
  • Organizer: 2nd Pacific Workshop on Discrete Mathematics
  • Place of Presentation: Tokai University Pacific Center, アアメリカ合衆国, ハワイ
  • Year and Date: 2005-12-08
• [Presentation] Geometric realiza-tion of projective triangulations with one face removed (2005)
  • Author(s): Atsuhiro Nakamoto
  • Organizer: 2nd Pacific Workshop on Discrete Mathematics
  • Place of Presentation: Tokai University Pacific Centerアメリカ合衆国, ハワイ
  • Year and Date: 2005-12-08
• [Presentation] Weigthed zeta functions of graphs (2005)
  • Author(s): Iwao Sato
  • Organizer: 2nd Pacific Workshop on Discrete Mathematics
  • Place of Presentation: Tokai University Pacific Centerアメリカ合衆国, ハワイ
  • Year and Date: 2005-12-08
• [Presentation] 閉曲面上の三角形分割の弛緩度と再埋蔵 (2005)
  • Author(s): 根上生也
  • Organizer: 第17回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2005-11-25
• [Presentation] 奇三角形分割におけるグラフの変形について (2005)
  • Author(s): 山本光
  • Organizer: 第17回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2005-11-25
• [Presentation] Geometoric realization of a projective triangulation with one face removed (2005)
  • Author(s): 中本敦浩
  • Organizer: 第17回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2005-11-25
• [Presentation] Lifts of automorphisms of symmetric digraphs associated with cycle ableian covers III (2005)
  • Author(s): 佐藤 巌
  • Organizer: 第17回位相幾何学的グラフ理論研究集会
  • Place of Presentation: 横浜国立大学
  • Year and Date: 2005-11-24
• [Presentation] Bartholdi zeta functions of graph coverings (2005)
  • Author(s): Iwao Sato
  • Organizer: Japan Worksho on Graph Theory and Combinatorics 2005-in hornor of Hikoe Enomoto's 60th birthday
  • Place of Presentation: 慶応義塾大学
  • Year and Date: 2005-06-21
• [Presentation] Looseness and indepen-dence number of maximal planar graphs (2005)
  • Author(s): Seiya Negami
  • Organizer: Japan Worksho on Graph Theory and Combinatorics 2005-in hornor of Hikoe Enomoto's 60th birthday
  • Place of Presentation: 慶応義塾大学
  • Year and Date: 2005-06-21
• [Presentation] N-Flips in even triangulations on surfaces (2005)
  • Author(s): Atsuhiro Nakamoto
  • Organizer: Japan Worksho on Graph Theory and Combinatorics 2005-in hornor of Hikoe Enomoto's 60th birthday
  • Place of Presentation: 慶応義塾大学
  • Year and Date: 2005-06-21
• [Presentation] Looseness and re-embedding structures of triangu-lations on closed surfaces (2005)
  • Author(s): Seiya Negami
  • Organizer: Graph Theory with Altitude, University of Colorado at Denver
  • Place of Presentation: アメリカ合衆国, デンバー
  • Year and Date: 2005-05-19
• [Presentation] 3-Colorable even triangulations on closed surfaces, Graph Theory with Altitude (2005)
  • Author(s): Atsuhiro Nakamoto
  • Organizer: University of Colorado at Denver
  • Place of Presentation: アメリカ合衆国, デンバー
  • Year and Date: 2005-05-19
• [Book] 人に教えたくなる数学-パズルを解くよりおもしろい (2007)
  • Author(s): 根上生也
  • Total Pages: 208
  • Publisher: ソフトバンク出版
• [Book] トポロジカル宇宙[完全版]-ポアンカレ予想解決への道 (2007)
  • Author(s): 根上生也
  • Total Pages: 205
  • Publisher: 日本評論社
• [Book] 計算しない数学, 計算する数学-ホントの数学は自分の中にある (2007)
  • Author(s): 根上生也, 桜井進
  • Total Pages: 200
  • Publisher: 技術評論社
• [Book] 計算しない数学-見えない"答え"が見えてくる! (2007)
  • Author(s): 根上生也
  • Total Pages: 216
  • Publisher: 青春出版社
• [Book] 人に教えたくなる数学 (2007)
  • Author(s): 根上生也
  • Total Pages: 208
  • Publisher: ソフトバンク出版
• [Book] 計算しない数学-見えない"答え"が見えてくる (2007)
  • Author(s): 根上生也
  • Total Pages: 216
  • Publisher: 青春出版社