A STUDY ON RELATIONSHIPS BETWEEN THE ERDOS-POSA PROPERTY AND DEGREE CONDITIONS IN GRAPHS

• Project/Area Number: 26800083
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kumamoto University
• Principal Investigator: CHIBA Shuya 熊本大学, 大学院先端科学研究部(工), 講師 (80579764)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000); Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: グラフ理論 / 点素な部分グラフ / 次数条件 / Erdos-Posa property / 閉路 / 星グラフ / 点素な閉路 / 2-因子 / 閉路による分割 / 点素な星グラフ / 最小次数条件 / 次数和条件 / 禁止部分グラフ

Outline of Final Research Achievements

In this research, I focused on the problem concerning relationships between the Erdos-Posa property and degree conditions for the existence of a prescribed number of vertex-disjoint subgraphs. In particular, I gave a conclusion for this problem in a sense by considering packing subgraphs in a graph under degree constraints. Moreover, I made progress in this research area by giving various sufficient conditions for partitioning a graph into cycles and for packing stars in a graph.

Research Products

• [Int'l Joint Research] University of West Bohemia(チェコ)
• [Int'l Joint Research] Lycee Craponne(France)
• [Int'l Joint Research] Shandong University(China)
• [Int'l Joint Research] Georgia State University(米国)
• [Journal Article] Vertex-disjoint copies of $K_{1,t} in $K_{1,r}$-free graphs (2017)
  • Author(s): Suyun Jiang, Shuya Chiba, Shinya Fujita, Jin Yan
  • Journal Title: Discrete Mathematics Volume: 340 Issue: 4 Pages: 649-654
  • DOI: 10.1016/j.disc.2016.11.034
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Degree sum conditions for vertex-disjoint cycles passing through specified vertices (2017)
  • Author(s): Shuya Chiba, Tomoki Yamashita
  • Journal Title: Discrete Mathematics Volume: 340 Issue: 4 Pages: 678-690
  • DOI: 10.1016/j.disc.2016.12.010
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Forbidden pairs with a common graph generating almost the same sets (2017)
  • Author(s): Shuya Chiba, Jun Fujisawa, Michitaka Furuya, Hironobu Ikarashi
  • Journal Title: Electronic Journal of Combinatorics Volume: 24
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Dominating cycles and forbidden pairs containing $P_{5}$ (2016)
  • Author(s): Shuya Chiba, Michitaka Furuya, Shoichi Tsuchiya
  • Journal Title: Graphs and Combinatorics Volume: 32 Issue: 5 Pages: 1773-1788
  • DOI: 10.1007/s00373-015-1673-8
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] emarks on upper and lower bounds for matching sequencibility of graphs (2016)
  • Author(s): Shuya Chiba, Yuji Nakano
  • Journal Title: FILOMAT Volume: 30 Issue: 8 Pages: 2091-2099
  • DOI: 10.2298/fil1608091c
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] 二部グラフ上の完全マッチングを含む2-因子と有向グラフ上の有向2-因子 (2016)
  • Author(s): 千葉 周也, 山下 登茂紀
  • Journal Title: 2016年度応用数学合同研究集会報告集 Volume: - Pages: 122-129
  • Acknowledgement Compliant
• [Journal Article] Equivalence of Jackson’s and Thomassen’s conjectures (2015)
  • Author(s): R. Cada, S. Chiba, K. Ozeki, P. Vrana and K. Yoshimoto
  • Journal Title: J. Combin. Theory Ser. B Volume: 印刷中 Pages: 124-147
  • DOI: 10.1016/j.jctb.2015.04.001
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Vertex-disjoint subgraphs with high degree sums (2015)
  • Author(s): Shuya Chiba, Nicolas Lichiardopol
  • Journal Title: Electronic Notes in Discrete Mathematics Volume: 49 Pages: 359-366
  • DOI: 10.1016/j.endm.2015.06.050
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] On lower bounds for matching sequencibility of general graphs (2015)
  • Author(s): Shuya Chiba
  • Journal Title: Proceedings of The 2015 Engineering Workshop among Ajou University, Shandong University and Kumamoto University Volume: - Pages: 52-52
• [Journal Article] Forbidden pairs and the existence of a dominating cycle (2015)
  • Author(s): Shuya Chiba, Michitaka Furuya, Shoichi Tsuchiya
  • Journal Title: Discrete Mathematics Volume: VOL.338 Issue: 12 Pages: 2442-2452
  • DOI: 10.1016/j.disc.2015.06.018
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A relationship between Thomassen's conjecture and Bondy's conjecture (2015)
  • Author(s): R. Cada, S. Chiba, K. Ozeki, P. Vrana and K. Yoshimoto
  • Journal Title: SIAM J. Discrete Math. Volume: 29 Issue: 1 Pages: 26-35
  • DOI: 10.1137/130937974
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Degree sum conditions for the circumference of 4-connected graphs (2014)
  • Author(s): S.Chiba, M.Tsugaki and T.Yamashita
  • Journal Title: Discrete Math. Volume: 333 Pages: 66-83
  • DOI: 10.1016/j.disc.2014.06.012
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] 二部グラフ上の完全マッチングを含む2-因子と有向グラフ上の有向2-因子 (2016)
  • Author(s): 千葉 周也, 山下 登茂紀
  • Organizer: 2016年度応用数学合同研究集会
  • Place of Presentation: 龍谷大学（滋賀県大津市）
  • Year and Date: 2016-12-16
• [Presentation] 2部グラフを経由したOreの定理の別証明 (2016)
  • Author(s): 津垣 正男, 斎藤 明, 山下 登茂紀, 千葉 周也, Guantao Chen, Xiaofeng Gu, Ron Gould
  • Organizer: 離散数学とその応用研究集会2016
  • Place of Presentation: 高城コミュニティセンター（宮城県宮城郡松島町）
  • Year and Date: 2016-08-22
• [Presentation] Minimum degree and forbidden subgraph conditions for disjoint stars in large graphs (2016)
  • Author(s): 千葉 周也, 藤田 慎也, Suyun Jiang, Jin Yan
  • Organizer: 離散数学とその応用研究集会2016
  • Place of Presentation: 高城コミュニティセンター（宮城県宮城郡松島町）
  • Year and Date: 2016-08-21
• [Presentation] On 2-factors through specified perfect matchings in bipartite graphs (2016)
  • Author(s): Shuya Chiba
  • Organizer: The Japanese Conference on Combinatorics and its Applications (JCCA 2016)
  • Place of Presentation: Kyoto University, Clock Tower Centennial Hall (Kyoto, Japan)
  • Year and Date: 2016-05-22
  • Int'l Joint Research
• [Presentation] 次数条件と2-因子について (2016)
  • Author(s): 千葉 周也
  • Organizer: RIMS 共同研究「閉曲面上のグラフの彩色問題への因子・閉路を利用してのアプローチ」
  • Place of Presentation: 京都大学数理解析研究所110号室
  • Year and Date: 2016-03-07
  • Invited
• [Presentation] Forbidden pairs of graphs generating almost the same sets (2016)
  • Author(s): Jun Fujisawa, Shuya Chiba, Michitaka Furuya, Hironobu Ikarashi
  • Organizer: The 4th Japan-Taiwan Conference on Combinatorics and its Applications
  • Place of Presentation: Kitakyushu International Conference Center, Room21 (Fukuoka, Japan)
  • Year and Date: 2016-03-05
  • Int'l Joint Research
• [Presentation] A degree sum condition on the order, the connectivity and the independence number for Hamiltonicity (2016)
  • Author(s): Masao Tsugaki, Shuya Chiba, Kenta Ozeki, Michitaka Furuya, Tomoki Yamashita
  • Organizer: The 4th Japan-Taiwan Conference on Combinatorics and its Applications
  • Place of Presentation: Kitakyushu International Conference Center, Room21 (Fukuoka, Japan)
  • Year and Date: 2016-03-05
  • Int'l Joint Research
• [Presentation] Degree conditions for 2-factors with k cycles in bipartite graphs (2016)
  • Author(s): Shuya Chiba
  • Organizer: The 4th Japan-Taiwan Conference on Combinatorics and its Applications
  • Place of Presentation: Kitakyushu International Conference Center, Room21 (Fukuoka, Japan)
  • Year and Date: 2016-03-05
  • Int'l Joint Research
• [Presentation] On dominating even subgraphs of cubic graphs II (2015)
  • Author(s): Roman Cada, 千葉 周也, 小関 健太, 善本 潔
  • Organizer: 2015年度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: 2015-12-17
• [Presentation] On lower bounds for matching sequencibility of general graphs (2015)
  • Author(s): Shuya Chiba
  • Organizer: The 2015 Engineering Workshop among Ajou University, Shandong University and Kumamoto University
  • Place of Presentation: Kumamoto University (Kumamoto, Japan)
  • Year and Date: 2015-11-12
  • Int'l Joint Research
• [Presentation] On disjoint subgraphs with high degree sums (2015)
  • Author(s): Shuya Chiba
  • Organizer: The Second Japan-Sino Symposium on Graph Theory, Combinatorics and Their Applications
  • Place of Presentation: Tokyo University of Science, Morito Memorial Hall (Tokyo, Japan)
  • Year and Date: 2015-11-02
  • Int'l Joint Research / Invited
• [Presentation] A degree sum condition on the order, the connectivity and the independence number for Hamiltonicity (2015)
  • Author(s): Shuya Chiba, Michitaka Furuya, Kenta Ozeki, Masao Tsugaki, Tomoki Yamashita
  • Organizer: The Second Japan-Sino Symposium on Graph Theory, Combinatorics and Their Applications
  • Place of Presentation: Tokyo University of Science, Morito Memorial Hall (Tokyo, Japan)
  • Year and Date: 2015-11-02
  • Int'l Joint Research
• [Presentation] Vertex-disjoint subgraphs with high degree sums (2015)
  • Author(s): Shuya Chiba, Nicolas Lichiardopol
  • Organizer: European Conference on Combinatorics, Graph Theory and Applications 2015 (EuroComb2015)
  • Place of Presentation: Hotel Grand Terminus (Norway, Bergen)
  • Year and Date: 2015-08-31
  • Int'l Joint Research
• [Presentation] On dominating even subgraphs of cubic graphs (2015)
  • Author(s): 善本 潔, Roman Cada, 千葉 周也, 小関 健太
  • Organizer: 離散数学とその応用研究集会2015
  • Place of Presentation: 熊本大学工学部百周年記念館
  • Year and Date: 2015-08-22
• [Presentation] グラフにおける次数条件と点素な閉路 (2015)
  • Author(s): 千葉 周也
  • Organizer: 第11回組合せ論若手研究集会
  • Place of Presentation: 慶應義塾大学 矢上キャンパス
  • Year and Date: 2015-03-05
  • Invited
• [Presentation] (g,f)-factors in directed graphs (2014)
  • Author(s): 千葉 周也，古谷 倫貴，太田 克弘，小関 健太
  • Organizer: 2014年度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: 2014-12-18
• [Presentation] 指定した頂点を含む閉路によるグラフの分割 (2014)
  • Author(s): 千葉 周也，山下 登茂紀
  • Organizer: 2014年度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: 2014-12-18
• [Presentation] Some remarks on upper and lower bounds for matching sequencibility of graphs (2014)
  • Author(s): Shuya Chiba
  • Organizer: The First Sino-Japan Symposium on Graph Theory, Combinatorics and their Applications
  • Place of Presentation: Academy of Mathematics and Systems Science, Beijing (China)
  • Year and Date: 2014-10-30
• [Presentation] ハミルトン閉路が存在するための次数和条件 (2014)
  • Author(s): 山下 登茂紀，千葉 周也，古谷 倫貴，小関 健太，津垣 正男
  • Organizer: 離散数学とその応用研究集会2014
  • Place of Presentation: 新潟総合テレビ・ゆめディア301～303
  • Year and Date: 2014-08-21
• [Presentation] 正則グラフの Matching Sequencibility について (2014)
  • Author(s): 千葉 周也
  • Organizer: 離散数学とその応用研究集会2014
  • Place of Presentation: 新潟総合テレビ・ゆめディア301～303
  • Year and Date: 2014-08-20
• [Presentation] Matching sequencibility of regular graphs (2014)
  • Author(s): 千葉 周也
  • Organizer: 第31回代数的組合せ論シンポジウム
  • Place of Presentation: 東北大学 片平さくらホール 2階会議室
  • Year and Date: 2014-06-19
• [Remarks] Kumamoto University
  • URL: https://kumamoto.pure.elsevier.com/en/persons/shuya-chiba