A study on the distance structure and the connectivity structure of graphs

2011 Fiscal Year Final Research Report

• Project/Area Number: 20340016
• 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: The University of Electro-Communications
• Principal Investigator: ANDO Kiyoshi 電気通信大学, 大学院・情報理工学研究科, 教授 (20096944)
• Co-Investigator(Kenkyū-buntansha): EGAWA Yoshimi 東京理科大学, 理学部, 教授 (70147502)
• Co-Investigator(Renkei-kenkyūsha): KAWARABAYASHI Ken-ichi 国立情報学研究所, 情報学プリンシプル研究系, 教授 (40361159)
• Project Period (FY): 2008 – 2011
• Keywords: 離散数学 / 組合せ論 / グラフ / 連結度 / 直径

Research Abstract

We studied on the distance structure and the connectivity structure of graphs. We obtained the upper bound of the number of degree 5 vertices in a 5-connected graph with critical connectivity structure. Also we found many new structural properties on 5-connected graphs and 6-connected graphs.

Research Products

• [Journal Article] Minimally contraction-critically 6-connected graphs (2012)
  • Author(s): Ando, Kiyoshi ; Fujita, Shinya ; Kawarabayashi, Ken-ichi
  • Journal Title: Discrete Math Volume: 312 Pages: 671-679
  • Peer Reviewed
• [Journal Article] Somestructural properties of minimally contraction-critically 5-connected graphs (2011)
  • Author(s): Ando Kiyoshi ; Chengfu, Qin
  • Journal Title: Discrete Math Volume: 311, no.13 Pages: 1084-1097
  • Peer Reviewed
• [Journal Article] Thenumber of vertices of degree 5 in acontraction-critically 5-connected graphs (2011)
  • Author(s): Ando, Kiyoshi ; Takashi Iwase
  • Journal Title: Discrete Math Volume: 311 Pages: 1925-1939
  • Peer Reviewed
• [Journal Article] Subgraph induced by theset of degree 5 vertices in a contraction critically 5-connected graph (2009)
  • Author(s): Ando, Kiyoshi
  • Journal Title: Discrete Math Volume: 309, no.22 Pages: 6359-6367
  • Peer Reviewed
• [Journal Article] A local structure theoremon 5-connected graphs (2009)
  • Author(s): Ando, Kiyoshi
  • Journal Title: J. Graph Theory Volume: 60, no.2 Pages: 99-129
  • Peer Reviewed
• [Journal Article] On the number of 4-contractibleedges in 4-connected graphs (2009)
  • Author(s): Ando, Kiyoshi ; Egawa, Yoshimi ; Kawarabayashi, Ken-ichi
  • Journal Title: J. Combin. Theory Ser. B Volume: 99, no.1 Pages: 97-109
  • Peer Reviewed
• [Journal Article] Edgesnot contained in triangles and the number of contractible edges in a 4-connectedgraph (2008)
  • Author(s): Ando, Kiyoshi ; Egawa, Yoshimi
  • Journal Title: Discrete Math Volume: 308, no.23 Pages: 3463-5472
  • Peer Reviewed
• [Journal Article] Edgesnot contained in triangles and the distribution of contractible edges in a4-connected graph (2008)
  • Author(s): Ando, Kiyoshi ; Egawa, Yoshimi
  • Journal Title: Discrete Math Volume: 308, no.16 Pages: 3449-3460
  • Peer Reviewed
• [Journal Article] Contractibleedges in minimally k-connected graphs (2008)
  • Author(s): Ando, Kiyoshi ; Kaneko, Atsushi ; Kawarabayash, Ken-ichi
  • Journal Title: Discrete Math Volume: 308, no.4 Pages: 597-602
  • Peer Reviewed
• [Presentation] Contractible edgesink-connected graphs (2012)
  • Author(s): Ando, Kiyoshi
  • Organizer: 日本数学会年会特別講演(招待講演)
  • Place of Presentation: 東京理科大神楽坂キャンパス
  • Year and Date: 2012-03-26
• [Presentation] Average degree of minimally contraction-critically6-connected graphs (2011)
  • Author(s): Ando, Kiyoshi
  • Organizer: 23th British Combinatorial Conference
  • Place of Presentation: Exeter/England
  • Year and Date: 2011-07-05
• [Presentation] An upper bound of the average degree of minimally contraction-critically 6-connected graphs (2010)
  • Author(s): Ando, Kiyoshi
  • Organizer: 3rd Pacific Workshop on Discrete Mathematics
  • Place of Presentation: Honolulu/USA
  • Year and Date: 2010-12-08
• [Presentation] Some structuralproperties of minimally contraction-critically 5-connectedgraphs (2010)
  • Author(s): Ando, Kiyoshi
  • Organizer: Combinatorics 2010
  • Place of Presentation: Verbania/Italy
  • Year and Date: 2010-06-28
• [Presentation] Wide diameter of k-connected graph with diameter (2009)
  • Author(s): Ando, Kiyoshi
  • Organizer: Japan conference of combinatorial geometry and graph theory 2009
  • Place of Presentation: 金沢文化ホール
  • Year and Date: 2009-11-12
• [Presentation] Some structuralproperties of a minimally contraction-critically 5-connected graph (2009)
  • Author(s): Ando, Kiyoshi
  • Organizer: 22nd British Combinatorial Conference
  • Place of Presentation: St. Andrews/Scotland
  • Year and Date: 2009-07-07
• [Presentation] The number of vertices of degree five in a contraction-critically 5-connected graph (2008)
  • Author(s): Ando, Kiyoshi
  • Organizer: Combinatorics 2008
  • Place of Presentation: Bologna/Italy
  • Year and Date: 2008-07-24