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

• 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 (ANDOU 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) ; 河原林 健一 国立情報学研究所, 情報学プリンシプル研究系, 准教授 (40361159)
• 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
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥10,010,000 (Direct Cost: ¥7,700,000、Indirect Cost: ¥2,310,000); Fiscal Year 2011: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2010: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000); Fiscal Year 2009: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000); Fiscal Year 2008: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
• 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] Minimally contraction-critically 6-connected graphs (2012)
  • Author(s): Ando, Kiyoshi; Fujita, Shinya; Kawarabayashi, Ken-ichi
  • Journal Title: Discrete Mathematics 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] The number of vertices of degree 5 in a contraction-critically 5-connected graph (2011)
  • Author(s): Ando, Kiyoshi; Iwase, Takashi
  • Journal Title: Discrete Mathematics Volume: 311 Pages: 1925-1939
  • Peer Reviewed
• [Journal Article] Some structural properties of minimally contraction-critically 5-connected graphs (2011)
  • Author(s): Ando, Kiyoshi, Qin, Chengfu
  • Journal Title: Discrete Mathematics 311 Pages: 1084-1097
• [Journal Article] Some structural properies of minimally contraction-critically 5-connected graphs (2011)
  • Author(s): K.Ando, Q.Chengfu
  • Journal Title: Discrete Mathematics Volume: 311 Pages: 1084-1097
  • 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] Subgraphs induced by the set of degree 5 vertices in a ccontractioncritically 5-connected graph (2009)
  • Author(s): K.Ando
  • Journal Title: Discrete Mathematics 309, no.22 Pages: 6359-6367
• [Journal Article] A local structure theorem on 5-connected graphs (2009)
  • Author(s): K.Ando
  • Journal Title: J.Graph Theory 60 no.2 Pages: 99-129
• [Journal Article] Subgraphs induced by the set of degree 5 vertices in a contraction-critically 5-connected graph (2009)
  • Author(s): K.Ando
  • Journal Title: Discrete Mathematics 309 Pages: 6359-6367
  • Peer Reviewed
• [Journal Article] A local structure theorem on 5-connected graphs (2009)
  • Author(s): K.Ando
  • Journal Title: J.Graph Theory 60 Pages: 99-129
  • Peer Reviewed
• [Journal Article] On the number of 4-contractible edges in 4-connected graphs (2009)
  • Author(s): K.Ando, Y.Egawa, K.Kawarabayashi, Kriesell.M
  • Journal Title: J.Combin.Theory Ser.B 99 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
• [Journal Article] On the number of 4-contractible edges in 4-connected graphs (2008)
  • Author(s): K.Ando, Y.Egawa, K.Kawarabayashi, Kriesell.M
  • Journal Title: J.Combin.Theory Ser.B 99 no.1 Pages: 97-109
• [Journal Article] Edges not contained in triangles and the number of contractible edges in a 4-connected graph (2008)
  • Author(s): K. Ando, Y. Egawa
  • Journal Title: Discrete Mathematics 308 Pages: 3463-3472
  • Peer Reviewed
• [Journal Article] Edges not contained in triangles and the distribution of contractible edges in a 4-connected graph (2008)
  • Author(s): K. Ando, Y. Egawa
  • Journal Title: Discrete Mathematics 308 Pages: 3449-3460
  • Peer Reviewed
• [Journal Article] Contractible edges in minimally $k$-connected graphs 4 (2008)
  • Author(s): K. Ando, A. kaneko, K. Kawarabayashi
  • Journal Title: Discrete Mathematics 308 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] Contractible edges in k-connected graphs (2012)
  • Author(s): K.Ando
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京理科大神楽坂キャンパス(特別講演)
  • Year and Date: 2012-03-26
• [Presentation] A local structure theorem on contraction-critically 6-connected graphs (2011)
  • Author(s): K.Ando
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学瀬田キャンパス
  • Year and Date: 2011-12-16
• [Presentation] The average degree of minimally contraction-critically 5-connected graphs (2011)
  • Author(s): K.Ando
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 信州大学松本キャンパス
  • Year and Date: 2011-09-28
• [Presentation] The average degree of minimally contraction-critically 5-connected graphs (2011)
  • Author(s): K.Ando
  • Organizer: 組み合わせ論サマーセミナー2011
  • Place of Presentation: 東京理科大学館山研修所
  • Year and Date: 2011-08-25
• [Presentation] The average degree of minimally contraction-critically 5-connected graphs (2011)
  • Author(s): K.Ando
  • Organizer: 離散数学とその応用研究集会2011
  • Place of Presentation: 奈良県文化会館
  • Year and Date: 2011-08-01
• [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] Average degree of minimally contraction-critically 6-connected graphs (2011)
  • Author(s): K.Ando
  • Organizer: 23nd British Combinatorial Conference
  • Place of Presentation: Exeter/England
  • Year and Date: 2011-07-05
• [Presentation] Minimally contraction-critically 6-connected graphs (2010)
  • Author(s): K.Ando
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学瀬田キャンパス
  • Year and Date: 2010-12-17
• [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] An upper bound of the average degree of minimally contraction-critically 6-connected graphs (2010)
  • Author(s): K.Ando
  • Organizer: 3^<rd> Pacific Workshop on Discrete Mathematics
  • Place of Presentation: Honolulu USA
  • Year and Date: 2010-12-08
• [Presentation] An upper bound of the average degree of minimally contraction-critically 6-connected graphs (2010)
  • Author(s): K.Ando
  • Organizer: 3rd Pacific Workshop on Discrete Mathematics
  • Place of Presentation: Honolulu/U.S.A.
  • Year and Date: 2010-12-07
• [Presentation] Minimally contraction-critically 6-connected graphs (2010)
  • Author(s): K.Ando
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学東山キャンパス
  • Year and Date: 2010-09-23
• [Presentation] Contraction-critically 5-connected graphについて (2010)
  • Author(s): K Ando
  • Organizer: 組み合わせ論サマーセミナー2009
  • Place of Presentation: 東京理科大学館山研修所
  • Year and Date: 2010-08-30
• [Presentation] Some structural properties of a minimally contraction-critically 6-conne cted graph (2010)
  • Author(s): K.Ando
  • Organizer: Combinatorics 2010
  • Place of Presentation: Verbania/Italy
  • Year and Date: 2010-06-30
• [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] Some structural properiea of minimally contraction-critically b-connected graphs (2010)
  • Author(s): K.Ando
  • Organizer: Combinatorics 2010
  • Place of Presentation: Verbania Italy
  • Year and Date: 2010-06-28
• [Presentation] Some structural properties of minimally contraction-critically 6-connected graphs (2010)
  • Author(s): K.Ando
  • Organizer: 日本数学会2010年総会
  • Place of Presentation: 慶応大学理工学部 (矢上キャンパス)
  • Year and Date: 2010-03-24
• [Presentation] Some structural properties of minimally contraction-critically 6-connected graphs (2010)
  • Author(s): K.Ando
  • Organizer: 岡村先生退職記念甲南大学研究集会
  • Place of Presentation: 甲南大学
  • Year and Date: 2010-03-06
• [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] Wide diameter of $k$-connected graph with diameter $d$ (2009)
  • Author(s): K.Ando
  • Organizer: JCCGG2009 (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] $k$-wide diameter of $k$-connected graph with diameter $d$ (2009)
  • Author(s): K.Ando
  • Organizer: 2009年度日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学豊中キャンパス
  • Year and Date: 2009-09-24
• [Presentation] A local structure theorem of contraction-critically 5-connected graphs (2009)
  • Author(s): K.Ando
  • Organizer: Micro symposium on combinatorics 2009
  • Place of Presentation: 南デンマーク大学/デンマーク
  • Year and Date: 2009-09-14
• [Presentation] The number of edges of a contraction-critically 5-connected graph (2009)
  • Author(s): K.Ando
  • Organizer: Hamburg 大学数学セミナー
  • Place of Presentation: Hamburg 大学/ドイツ
  • Year and Date: 2009-09-12
• [Presentation] A structural result on minimally contraction-critically 6-connected graphs (2009)
  • Author(s): K.Ando
  • Organizer: 組み合わせ論サマーセミナー2009
  • Place of Presentation: 東京理科大学館山研修所
  • Year and Date: 2009-09-03
• [Presentation] Wide diameter of $k$-connected graphs with diameter $d$ (2009)
  • Author(s): K.Ando
  • Organizer: 離散数学とその応用研究集会2009
  • Place of Presentation: 茨城大学工学部 (日立キャンパス)
  • Year and Date: 2009-08-08
• [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] Some structural properties of a minimally contraction-critically 5-conne cted graph (2009)
  • Author(s): K.Ando
  • Organizer: The 22th British Combinatorial Conference
  • Place of Presentation: St.Andrews/Scotland
  • Year and Date: 2009-07-07
• [Presentation] Some structural properties of a minimally contraction-critically 5-connected graph (2009)
  • Author(s): K.Ando
  • Organizer: The 22th British Combinatorial Conference at St. Andrews
  • Place of Presentation: St. Andrews /Scotland
  • Year and Date: 2009-07-07
• [Presentation] Minimally Contraction-Critically 5-Connected Graphs (2009)
  • Author(s): K.Ando
  • Organizer: Conference in Honor of Dr. Severino Gervacio 2009 (SVGCGTC2009)
  • Place of Presentation: フィリピン、マニラ、デラサール大学
  • Year and Date: 2009-04-25
• [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