On Graphs, Even graphs and interaction between minimum degree and connectivity

• Project/Area Number: 18540142
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Nihon University
• Principal Investigator: YOSHIMOTO Kiyoshi (YOSHIMOTO Kiyoshl) Nihon University, 理工学部, 講師 (90307801)
• Project Period (FY): 2006 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥3,990,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥690,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: 線グラフ / クローフリーグラフ / ハミルトンサイクル / 2因子 / 偶グラフ / Claw-free graph / line graph / 独立点集合 / 連結度 / Claw-freegraph / hami1ton cycle / Hamilton cycle / グラフ理論 / claw-free graph / Ore型条件 / 最小次数 / 独立店集合 / claw-freeグラフ

Research Abstract

The existence of 2-factors of claw-free graphs can be determined by minimum degree condition without connectivity. In this research, by using Ryjacek closure, we replace problems on 2-factors in claw-free graphs with 2-factors of line graphs or the preimage graphs and analyzed structures of claw-free graphs.

Research Products

• [Journal Article] Sharp upper bounds for the minimum number of components of 2-factors in claw-free graphs (2009)
  • Author(s): H.J. Broersma, D. Paulusma, K. Yoshimoto
  • Journal Title: Graphs Combin 25 Pages: 427-460
  • Peer Reviewed
• [Journal Article] Spanning Even Subgraphs of 3-edge-connected Graphs (2009)
  • Author(s): B. Jackson, K. Yoshimoto
  • Journal Title: J. Graph Theory 62 Pages: 37-47
  • Peer Reviewed
• [Journal Article] Sharp upper bounds for the minimum number of componentsof 2-factors in claw-free graphs (2009)
  • Author(s): H. J. Broersma, D. Paulusma, K. Yoshimoto
  • Journal Title: Graphs Combin. (出版決定)(予定)
  • Peer Reviewed
• [Journal Article] Spanning Even Subgraphs of 3-edge-connected Graphs (2009)
  • Author(s): B. Jackson, K. Yoshimoto
  • Journal Title: J. Graph Theory (出版決定)(予定)
  • Peer Reviewed
• [Journal Article] An Extremal Problem Resulting in Many Paths (2009)
  • Author(s): R. H. Schelp, K. Yoshimoto
  • Journal Title: Ars Combin. (出版決定)(予定)
  • Peer Reviewed
• [Journal Article] λ-Backbone Colorings Along Pairwise Disjoint Stars and Matchings (2009)
  • Author(s): H. J. Broersma, J. Fujisawa, L. Marchal, D. Paulusma, A. N. M. Salman, K. Yoshimoto
  • Journal Title: Discrete Math. (出版決定)(予定)
  • Peer Reviewed
• [Journal Article] Edge degrees and dominating cycles (2008)
  • Author(s): K. Yoshimoto
  • Journal Title: Discrete Math 308 Pages: 2594-2599
  • Peer Reviewed
• [Journal Article] On a spanning tree with specified leaves (2008)
  • Author(s): Y. Egawa, H. Matsuda, T. Yamashita, K. Yoshimoto
  • Journal Title: Graphs Combin 24 Pages: 13-18
  • Peer Reviewed
• [Journal Article] Edge degrees and dominating cycles (2008)
  • Author(s): K. Yoshimoto
  • Journal Title: Discrete Math. 308 Pages: 2594-2599
  • Peer Reviewed
• [Journal Article] On a spanning tree with specified leaves (2008)
  • Author(s): Y. Egawa, H. Matsuda, T. Yamashita, K. Yoshimoto
  • Journal Title: Graphs Combin. 24 Pages: 13-18
  • Peer Reviewed
• [Journal Article] Relative length of longest paths and longest cycles in a triangle-free graph (2007)
  • Author(s): D. Paulusma, K. Yoshimoto
  • Journal Title: Discrete Math 308 Pages: 1222-1229
  • Peer Reviewed
• [Journal Article] On the number of components in 2-factors of claw-free graphs (2007)
  • Author(s): K. Yoshimoto
  • Journal Title: Discrete Math 307 Pages: 2808-2819
  • Peer Reviewed
• [Journal Article] Even subgraphs of bridgeless graphs and 2-factors of line graphs (2007)
  • Author(s): B. Jackson, K. Yoshimoto
  • Journal Title: Discrete Math 307 Pages: 2775-2785
  • Peer Reviewed
• [Journal Article] Cycles through specified vertices in a triangle-free graph (2007)
  • Author(s): D. Paulusma, K. Yoshimoto
  • Journal Title: Discuss. Math. Graph Theory 27 Pages: 179-192
  • Peer Reviewed
• [Journal Article] Toughness and hamiltonicity in k-trees (2007)
  • Author(s): H. Broersma, L. Xiong, K. Yoshimoto
  • Journal Title: Discrete Math 307 Pages: 832-838
  • Peer Reviewed
• [Journal Article] The upper bound of the number of cycles in a 2-factor of a line graph (2007)
  • Author(s): J. Fujisawa, L. Xiong, K. Yoshimoto, S. Zhang
  • Journal Title: J. Graph Thoery 55 Pages: 72-82
  • Peer Reviewed
• [Journal Article] Relative length of longest paths and longest cycles in a triangle-free graph (2007)
  • Author(s): D. Paulusma and K. Yoshimoto
  • Journal Title: Discrete Math. 308 Pages: 1222-1229
  • Peer Reviewed
• [Journal Article] On the number of Components in 2-factors of claw-free graphs (2007)
  • Author(s): K. Yoshimoto
  • Journal Title: Discrete Math. 307 Pages: 2808-2819
  • Peer Reviewed
• [Journal Article] Even subgraphs of bridgeless graphs and 2-factors of line graphs (2007)
  • Author(s): B. Jackson and K. Yoshimoto
  • Journal Title: Discrete Math. 307 Pages: 2775-2785
  • Peer Reviewed
• [Journal Article] The upper bound of the number Of cycles in a 2-factor of a line graph (2007)
  • Author(s): J. Fujisawa, L. Xiong, K. Yoshimoto and S. Zhang
  • Journal Title: J. Graph Thoery 55 Pages: 72-82
  • Peer Reviewed
• [Journal Article] The upper bound of the number of cycles in a 2-factor of a line graph (2007)
  • Author(s): K. Yoshimoto, et. al.
  • Journal Title: J. Graph Theory 55 Pages: 72-82
  • Peer Reviewed
• [Journal Article] Toughness and hamiltonicity in k-trees (2007)
  • Author(s): K. Yoshimoto, et. al.
  • Journal Title: Discrete Math. 307 Pages: 832-838
  • Peer Reviewed
• [Journal Article] On the number of components in 2-factors of claw-free graphs (2007)
  • Author(s): K. Yoshimoto
  • Journal Title: Discrete Math. 307 Pages: 2808-2819
  • Peer Reviewed
• [Journal Article] Set-ordered as a generalization of k-ordered
  • Author(s): K. Ishii, K. Ozeki, K. Yoshimoto
  • Journal Title: Discrete Math. (to appear)
  • Peer Reviewed
• [Journal Article] Closure concept for 2-factors in claw-free graphs
  • Author(s): Z. Ryjacek, L. Xing, K. Yoshimoto
  • Journal Title: Discrete Math. (to appear)
  • Peer Reviewed
• [Journal Article] A 2-factor in which each cycle contains a vertex in a specified stable set
  • Author(s): S. Chiba, Y. Egawa, K. Yoshimoto
  • Journal Title: Australas. J. Combin. (to appear)
  • Peer Reviewed
• [Journal Article] An Extremal Problem Resulting in Many Paths
  • Author(s): R.H. Schelp, K. Yoshimoto
  • Journal Title: Ars Combin. (to appear)
  • Peer Reviewed
• [Journal Article] λ-Backbone Colorings Along Pairwise Disjoint Stars and Matchings
  • Author(s): H.J. Broersma, J. Fujisawa, L. Marchal, D. Paulusma, A.N.M. Salman, K. Yoshimoto
  • Journal Title: Discrete Math (to appear)
  • Peer Reviewed
• [Journal Article] Closure concept for 2-factors in claw-free graphs
  • Author(s): Z.Ryjacek, L.Xing, K.Yoshimoto
  • Journal Title: Discrete Math. (印刷中)
  • Peer Reviewed
• [Journal Article] A 2-factor in which each cycle contains a vertex in a specified stable set
  • Author(s): S.Chiba, Y.Egawa, K.Yoshimoto
  • Journal Title: Australas.J.Combin. (印刷中)
  • Peer Reviewed
• [Journal Article] An Extremal Problem Resulting in Many Paths
  • Author(s): R.H.Schelp, K.Yoshimoto
  • Journal Title: Ars Combin. (印刷中)
  • Peer Reviewed
• [Journal Article] Spanmig Even Subgraphs of 3-edge-Connected Graphs
  • Author(s): B. Jackson and K. Yoshimoto
  • Journal Title: J. GraphTheory to appear
  • Peer Reviewed
• [Journal Article] The upper bound of the number of cycles in a 2-factor of a line graph
  • Author(s): J.Fujisawa, L.Xiong, K.Yoshimoto, S.Zhang
  • Journal Title: J. Graph Thoery To Appear
• [Journal Article] Toughness and hamiltonicity in k-trees
  • Author(s): H.Broersma, L.Xiong, K.Yoshimoto
  • Journal Title: Discrete Math. To Appear
• [Journal Article] Cycles through specified vertices in a triangle-free graph
  • Author(s): D.Paulusma, K.Yoshimoto
  • Journal Title: Discuee. Math. Graph Theory To Appear
• [Presentation] On independent sets and 2-factors of claw-free graphs (2009)
  • Author(s): 善本潔
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学
  • Year and Date: 2009-12-15
• [Presentation] Claw-free graphs and 2-factors that separate independent vertices (2009)
  • Organizer: Oddeleni diskretni matematiky
  • Place of Presentation: University of West Bohemia, Czech
  • Year and Date: 2009-04-10
• [Presentation] On 2-factors of claw-free graphs (2008)
  • Place of Presentation: Beijing Inst. of Tech., China
  • Year and Date: 2008-12-21
• [Presentation] On independent sets and 2-factors of claw-free graphs (2008)
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大
  • Year and Date: 2008-12-17
• [Presentation] On 2-factors of claw-free graphs (2008)
  • Organizer: 5th Workshop on the Matthews-Sumner Conjecture and Related Problems
  • Place of Presentation: Domazlice, Czech
  • Year and Date: 2008-10-12
• [Presentation] On 2-factors of claw-free graphs (招待講演) (2008)
  • Author(s): 善本 潔
  • Organizer: 5th Workshop on the Matthews-Sumner Conjecture and Related Problems
  • Place of Presentation: チェコ
  • Year and Date: 2008-10-10
• [Presentation] On Claw-free graphs and Cubic graphs (2008)
  • Organizer: 日本数学会
  • Place of Presentation: 東工大
  • Year and Date: 2008-09-24
• [Presentation] On Claw-free graphs and Cubic graphs (特別講演) (2008)
  • Author(s): 善本 潔
  • Organizer: 日本数学会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-24
• [Presentation] 2因子とハミルトンサイクルについて (2008)
  • Organizer: 第4回組合せ論若手研究集会
  • Place of Presentation: 慶應大
  • Year and Date: 2008-02-05
• [Presentation] 2因子とハミルトンサイクルについて(招待講演) (2008)
  • Author(s): 善本 潔
  • Organizer: 第4回組合せ論若手研究集会
  • Place of Presentation: 慶應義塾大学矢上キャパス
  • Year and Date: 2008-02-05
• [Presentation] 2-factors of claw-free graphs (2008)
  • Author(s): 善本潔
  • Organizer: 5th workshop on the Matthews-Sumner Conjecture and Related Problems
  • Place of Presentation: Domazlice, Czech
• [Presentation] On Claw-free graphs and Cubic graphs (2008)
  • Author(s): 善本潔
  • Organizer: 日本数学会
  • Place of Presentation: 東工大(特別講演)
• [Presentation] 2因子とハミルトンサイクルについて (2008)
  • Author(s): 善本潔
  • Organizer: 第4同組合せ論若手研究集会
  • Place of Presentation: 慶鷹大(招待講演)
• [Presentation] A 2-factor in which each cycle contains a vertex in a specified stable set (2007)
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大
  • Year and Date: 2007-12-19
• [Presentation] Path cover number and Crowded cycles (2007)
  • 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] On the number of components in 2-factors of claw-free graphs III (2007)
  • Organizer: The Kyoto International Conference on Computational Geometry and Graph Theory
  • Place of Presentation: Kyoto Univ., Japan
  • Year and Date: 2007-06-12
• [Presentation] (S_1, ., ., S_l)-ordered cycles and crowded paths (2007)
  • Organizer: Extremal Combinatorics Workshop
  • Place of Presentation: Renyi Institute, Budapest, Hungary
  • Year and Date: 2007-06-04
• [Presentation] On the number of components in 2-factors of claw-free graphs III (2007)
  • Organizer: 38th Southeastern International Conference on Combinatorics
  • Place of Presentation: Florida Atlantic Univ. Florida, USA
  • Year and Date: 2007-04-08
• [Presentation] (S_1, ...S_1)-ordered cycles and crowded paths (2007)
  • Author(s): 善本潔
  • Organizer: Extremal Combinatorics Workshop
  • Place of Presentation: Renyi Institute, Budapest, Hungary
• [Presentation] On the number of components in 2-Tfactors of claw-free graphs III (2007)
  • Author(s): 善本潔
  • Organizer: 38th Southeastern International Conference on Combinatorics, Graph Theory, and Computing
  • Place of Presentation: Florida Atlantic Univ. Florida, USA
• [Presentation] (S_1,., S_1)-ordered cycles and crowded paths (2007)
  • Author(s): K. Yoshimoto
  • Organizer: Extremal Combinatorics Workshop
  • Place of Presentation: Renyi Institute, Budapest
• [Remarks]
  • URL: http://www.math.cst.nihon-u.ac.jp/~yosimoto/math.html