A study for finding a new approach toward Ramsey-type problems in graphs

• Project/Area Number: 15K04979
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Yokohama City University
• Principal Investigator: FUJITA SHINYA 横浜市立大学, データサイエンス学部, 准教授 (60424206)
• Project Period (FY): 2015-04-01 – 2019-03-31
• Project Status: Completed (Fiscal Year 2018)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: グラフの極値問題 / ラムゼー数 / ラムゼー型問題 / グラフの辺着色 / グラフの安全集合 / グラフのラムゼー数 / グラフの彩色問題 / グラフの分割問題 / 密なグラフの部分構造 / グラフのラムゼー型問題 / 辺着色

Outline of Final Research Achievements

In this research project, I explored a new approach toward the Ramsey-type problems in graphs. As a result, I obtained some new results that could be useful tools to tackle
some of the Ramsey-type problems in graphs.

Academic Significance and Societal Importance of the Research Achievements

ラムゼー型問題の解決には単色の部分構造の解析が重要であるため，本研究を進める上でグラフの安全集合という新しい概念を提起して全く新しいアプローチから研究を推進した．その結果，ラムゼー型問題に留まらずグラフ理論の幅広い分野で適用可能な定理を多数得ることが出来た．グラフの安全集合の概念はグラフアルゴリズムの研究者グループの注目を惹き，本研究から国内外で活発に研究がなされるような波及効果を生み出すテーマを提供することが出来た．また，肝心のグラフのラムゼー型問題についても，辺着色グラフ上の分割問題に関するある予想を提起し，その部分的解決を与えることで注目度の高い研究成果を与えることが出来た．

Research Products

• [Int'l Joint Research] 中山大学(中国)
• [Int'l Joint Research] ウェストボヘミア大学(チェコ)
• [Int'l Joint Research] 西北工業大学(中国)
• [Int'l Joint Research] 西北工業大学(中国)
• [Journal Article] A new approach towards a conjecture on intersecting three longest paths (2019)
  • Author(s): Fujita Shinya、Furuya Michitaka、Naserasr Reza、Ozeki Kenta
  • Journal Title: Journal of Combinatorics Volume: 10 Issue: 2 Pages: 221-234
  • DOI: 10.4310/joc.2019.v10.n2.a2
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On the weighted safe set problem on paths and cycles (2018)
  • Author(s): Fujita Shinya、Jensen Tommy、Park Boram、Sakuma Tadashi
  • Journal Title: Journal of Combinatorial Optimization Volume: 37 Issue: 2 Pages: 685-701
  • DOI: 10.1007/s10878-018-0316-4
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Safe number and integrity of graphs (2018)
  • Author(s): Fujita Shinya、Furuya Michitaka
  • Journal Title: Discrete Applied Mathematics Volume: 247 Pages: 398-406
  • DOI: 10.1016/j.dam.2018.03.074
  • Peer Reviewed
• [Journal Article] Bounding the distance among longest paths in a connected graph (2018)
  • Author(s): Ekstein Jan、Fujita Shinya、Kabela Adam、Teska Jakub
  • Journal Title: Discrete Mathematics Volume: 341 Issue: 4 Pages: 1155-1159
  • DOI: 10.1016/j.disc.2017.09.029
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Kernels by properly colored paths in arc-colored digraphs (2018)
  • Author(s): Bai Yandong、Fujita Shinya、Zhang Shenggui
  • Journal Title: Discrete Mathematics Volume: 341 Issue: 6 Pages: 1523-1533
  • DOI: 10.1016/j.disc.2018.02.014
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Highly connected subgraphs of graphs with given independence number (2018)
  • Author(s): Fujita Shinya、Liu Henry、Sarkar Amites
  • Journal Title: European Journal of Combinatorics Volume: 70 Pages: 212-231
  • DOI: 10.1016/j.ejc.2018.01.004
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Color degree and monochromatic degree conditions for short properly colored cycles in edge-colored graphs (2017)
  • Author(s): Fujita Shinya、Li Ruonan、Zhang Shenggui
  • Journal Title: Journal of Graph Theory Volume: 87 Issue: 3 Pages: 362-373
  • DOI: 10.1002/jgt.22163
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Decomposing edge-colored graphs under color degree constraints (2017)
  • Author(s): Fujita Shinya、Li Ruonan、Wang Guanghui
  • Journal Title: Electronic Notes in Discrete Mathematics Volume: 61 Pages: 491-497
  • DOI: 10.1016/j.endm.2017.06.078
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Safe sets, network majority on weighted trees (2017)
  • Author(s): Bapat Ravindra B.、Fujita Shinya、Legay Sylvain、Manoussakis Yannis、Matsui Yasuko、Sakuma Tadashi、Tuza Zsolt
  • Journal Title: Networks Volume: 71 Issue: 1 Pages: 81-92
  • DOI: 10.1002/net.21794
  • Peer Reviewed / Int'l Joint Research
• [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] Non-separating subgraphs in highly connected graphs (2016)
  • Author(s): Shinya Fujita, Ken-ichi Kawarabayashi
  • Journal Title: Journal of Combinatorial Theory Series B Volume: 117 Pages: 1-21
  • DOI: 10.1016/j.jctb.2015.12.001
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Highly Connected Subgraphs of Graphs with Given Independence Number (Extended Abstract) (2016)
  • Author(s): Shinya Fujita, Henry Liu, Amites Sarkar
  • Journal Title: Electronic Notes in Discrete Mathematics Volume: 54 Pages: 103-108
  • DOI: 10.1016/j.endm.2016.09.019
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Safe set problem on graphs (2016)
  • Author(s): Shinya Fujita, Gary MacGillivray, Tadashi Sakuma
  • Journal Title: Discrete Applied Mathematics Volume: 215 Pages: 106-111
  • DOI: 10.1016/j.dam.2016.07.020
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Partitioning a graph into highly connected subgraphs (2016)
  • Author(s): Valentin Borozan, Michael Ferrara, Shinya Fujita, Michitaka Furuya, Yannis Manoussakis, Narayanan N, Derrick Stolee
  • Journal Title: Journal of Graph Theory Volume: 82 Issue: 3 Pages: 322-333
  • DOI: 10.1002/jgt.21904
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] From Edge-Coloring to Strong Edge-Coloring (2015)
  • Author(s): Valentin Borozan, Gerard Jennhwa Chang, Nathann Cohen, Shinya Fujita, Narayanan Narayanan, Reza Naserasr, Petru Valicov
  • Journal Title: Electronic Journal of Combinatorics Volume: 22
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Presentation] 連結グラフの optimal proper connection number について (2019)
  • Author(s): 藤田慎也
  • Organizer: 日本数学会2019年度年会
• [Presentation] Some recent results on safe set problems in vertex-weighted graphs (2019)
  • Author(s): 藤田慎也
  • Organizer: AMS Meeting
  • Int'l Joint Research
• [Presentation] On the weighted safe set problem on paths and cycles (2018)
  • Author(s): 藤田慎也、Tommy Jensen、Boram Park、佐久間雅
  • Organizer: 日本数学会2018年度秋季総合分科会
• [Presentation] 辺着色グラフの proper connection number に関する研究の進展 (2018)
  • Author(s): 藤田慎也
  • Organizer: 2018年度応用数学合同研究集会
• [Presentation] Kernels by properly colored paths in arc-colored digraphs (2018)
  • Author(s): Yandong Bai, 藤田慎也, Shenggui Zhang
  • Organizer: 日本数学会2018年度年会
• [Presentation] 辺着色グラフの分割問題 (2017)
  • Author(s): 藤田慎也
  • Organizer: 2017年度日本数学会年会
  • Place of Presentation: 首都大学東京（東京都八王子市）
  • Year and Date: 2017-03-24
• [Presentation] 辺着色グラフの次数条件と閉路の存在について (2017)
  • Author(s): 藤田慎也
  • Organizer: 日本数学会2017年度秋季総合分科会
• [Presentation] Decomposing edge-colored grapus under color degree constraints (2017)
  • Author(s): Shinya Fujita, Ruonan Li, Guanghui Wang
  • Organizer: European Conference on Combinatorics, Graph Theory and Applications (Eurocomb 2017)
  • Int'l Joint Research
• [Presentation] Bounding the distance among longest paths in a connected graph (2017)
  • Author(s): Jan Ekstein, 藤田慎也, Adam Kabela, Jakub Teska
  • Organizer: 2017年度応用数学合同研究集会
• [Presentation] Color degree and monochromatic degree conditions for short properly colored cycles (2016)
  • Author(s): 藤田慎也
  • Organizer: The Third Sino-Japan Symposium on Graph Theory, Combinatorics and their Applications
  • Place of Presentation: 西北工業大学（西安市，中国）
  • Year and Date: 2016-11-03
  • Int'l Joint Research
• [Presentation] Partitioning a graph into dense parts (2016)
  • Author(s): 藤田慎也
  • Organizer: 2016 International Conference on Graph Theory, Combinatorics and Applications
  • Place of Presentation: Zhejiang Normal University(金華市，中国）
  • Year and Date: 2016-10-29
  • Int'l Joint Research / Invited
• [Presentation] Some results on properly colored cycles in edge-colored graphsⅡ（続報） (2016)
  • Author(s): 藤田慎也
  • Organizer: 2016年度日本数学会秋季総合分科会
  • Place of Presentation: 関西大学（大阪府吹田市）
  • Year and Date: 2016-09-15
• [Presentation] Highly Connected Subgraphs of Graphs with Given Independence Number (2016)
  • Author(s): Shinya Fujita, Henry Liu, Amites Sarkar
  • Organizer: Discrete Mathematics Days
  • Place of Presentation: カタルーニャ工科大学（バルセロナ，スペイン）
  • Year and Date: 2016-07-06
  • Int'l Joint Research
• [Presentation] Some results on properly colored cycles in edge-colored graphs (2016)
  • Author(s): 藤田慎也
  • Organizer: 2016年度日本数学会年会
  • Place of Presentation: 筑波大学
  • Year and Date: 2016-03-16
• [Presentation] Highly connected subgraphs of graphs with given independence number (2015)
  • Author(s): Shinya Fujita, Henry Liu, Amites Sarkar
  • Organizer: 2015年度応用数学合同研究集会
  • Place of Presentation: 龍谷大学
  • Year and Date: 2015-12-17
• [Presentation] A New Approach Towards a Conjecture on Intersecting Three Longest Paths (2015)
  • Author(s): Shinya Fujita
  • Organizer: The second Japan-Sino Symposium on Graph Theory, Combinatorics and Their Applications
  • Place of Presentation: 東京理科大学
  • Year and Date: 2015-11-02
  • Int'l Joint Research
• [Presentation] A New Approach Towards a Conjecture on Intersecting Three Longest Paths (2015)
  • Author(s): Shinya Fujita, Michitaka Furuya, Reza Naserasr, Kenta Ozeki
  • Organizer: 2015年度日本数学会秋季総合分科会
  • Place of Presentation: 京都産業大学
  • Year and Date: 2015-09-13