• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

A study on partition problems in edge-colored graphs

Research Project

Project/Area Number 19K03603
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12030:Basic mathematics-related
Research InstitutionYokohama 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) 2019-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2022: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords辺着色グラフ / グラフの分割問題 / グラフの次数条件 / グラフの極値問題 / グラフのラムゼー数 / グラフの彩色問題 / 密なグラフの部分構造
Outline of Research at the Start

本研究は、申請者が最近の研究で提起した辺着色グラフの分割問題に関する予想について、部分的、もしくは可能であれば全面的に解決することを目標としている。研究では、国内外の研究者たちとの学術交流の機会を大事にしながら、多角的視点により予想の解決を目指したい。
さらに、本研究では、当該予想の解決に向けた考察過程で得られた知見を活かすことで、辺着色グラフの枠組みを超えて密なグラフの内部構造が把握出来るような、グラフ理論において汎用性の高い構造定理についてもその構築を狙っていきたい。

Outline of Final Research Achievements

In this work, we studied a graph partition problem in edge-colored graphs. For an edge-colored graph G and a vertex v in G, we define the color degree of v, which means the number of colors adjacent to v in G. There is a open problem concerning partitioning G into two parts such that each part satisfies some color degree conditions. We tackled the problem and obtained some new results in this area of study.

Academic Significance and Societal Importance of the Research Achievements

グラフの頂点集合を二つの部分集合に分割し、各パートで誘導されるグラフがある条件を満たすようにするといったグラフの分割問題は重要であり、様々な関連問題に関する研究が国内外で盛んに進められている。本研究はこのようなグラフの分割問題を辺着色グラフ上で考察し、構造的グラフ理論の研究で有用な補題となり得るいくつかの定理を証明することに成功した。グラフ理論の問題は頂点数に関する帰納法で解かれることが多いため、当該分野の研究は重要であり、得られた研究成果は離散数学の様々な場面で応用が期待できると思われる。

Report

(6 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (37 results)

All 2023 2022 2021 2020 2019 Other

All Int'l Joint Research (9 results) Journal Article (9 results) (of which Int'l Joint Research: 7 results,  Peer Reviewed: 9 results) Presentation (19 results) (of which Int'l Joint Research: 7 results,  Invited: 3 results)

  • [Int'l Joint Research] Ajou University(韓国)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Sun Yat-sen University(中国)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] University of Strathclyde(英国)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Ajou University(韓国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] University of Strathclyde(英国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Sun Yat-sen University(中国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] University of Southern Denmark(デンマーク)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Ajou University(韓国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] 山東大学/西北工業大学/中山大学(中国)

    • Related Report
      2019 Research-status Report
  • [Journal Article] Minimum Number of Edges Guaranteeing the Existence of a $K_{1, t}$-Factor in a Graph2023

    • Author(s)
      Shuya Chiba, Yoshimi Egawa, Shinya Fujita
    • Journal Title

      Graphs and Combinatorics

      Volume: 39 Issue: 2

    • DOI

      10.1007/s00373-023-02616-0

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The optimal proper connection number of a graph with given independence number2021

    • Author(s)
      Fujita Shinya、Park Boram
    • Journal Title

      Discrete Optimization

      Volume: 41 Pages: 100660-100660

    • DOI

      10.1016/j.disopt.2021.100660

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Stable structure on safe set problems in vertex-weighted graphs2021

    • Author(s)
      Fujita Shinya、Park Boram、Sakuma Tadashi
    • Journal Title

      European Journal of Combinatorics

      Volume: 91 Pages: 103211-103211

    • DOI

      10.1016/j.ejc.2020.103211

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On Properly Ordered Coloring of Vertices in a Vertex-Weighted Graph2021

    • Author(s)
      Fujita Shinya、Kitaev Sergey、Sato Shizuka、Tong Li-Da
    • Journal Title

      Order

      Volume: 38 Issue: 3 Pages: 515-525

    • DOI

      10.1007/s11083-021-09554-7

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Optimal proper connection of graphs2020

    • Author(s)
      Fujita Shinya
    • Journal Title

      Optimization Letters

      Volume: 14 Issue: 6 Pages: 1371-1380

    • DOI

      10.1007/s11590-019-01442-9

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Stable Structure on Safe Set Problems in Vertex-Weighted Graphs II --Recognition and Complexity--2020

    • Author(s)
      Fujita Shinya、Park Boram、Sakuma Tadashi
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 12301 Pages: 364-375

    • DOI

      10.1007/978-3-030-60440-0_29

    • ISBN
      9783030604394, 9783030604400
    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Decomposing edge-coloured graphs under colour degree constraints2019

    • Author(s)
      Fujita Shinya、Li Ruonan、Wang Guanghui
    • Journal Title

      Combinatorics, Probability and Computing

      Volume: 28 Issue: 5 Pages: 755-767

    • DOI

      10.1017/s0963548319000014

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] General upper bounds on independent k-rainbow domination2019

    • Author(s)
      Shinya Fujita, Michitaka Furuya, Colton Magnant
    • Journal Title

      Discrete Applied Mathematics

      Volume: 258 Pages: 105-113

    • DOI

      10.1016/j.dam.2018.11.018

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On sufficient conditions for rainbow cycles in edge-colored graphs2019

    • Author(s)
      Fujita Shinya、Ning Bo、Xu Chuandong、Zhang Shenggui
    • Journal Title

      Discrete Mathematics

      Volume: 342 Issue: 7 Pages: 1956-1965

    • DOI

      10.1016/j.disc.2019.03.012

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Recent progress on non-separating subgraphs in highly connected graphs2023

    • Author(s)
      Shinya Fujita
    • Organizer
      ICIAM 2023
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Safe set problems in vertex-weighted graphs and digraphs2023

    • Author(s)
      Shinya Fujita
    • Organizer
      The 3rd East Asia Workshop on Extremal and Structural Graph Theory
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 頂点加重グラフ上への proper orientation number の拡張問題2023

    • Author(s)
      藤田慎也、飯田礼美子、前澤俊一
    • Organizer
      応用数学合同研究集会2023
    • Related Report
      2023 Annual Research Report
  • [Presentation] Connectivity keeping paths in highly connected graphs2023

    • Author(s)
      藤田慎也
    • Organizer
      日本数学会2023年度年会
    • Related Report
      2022 Research-status Report
  • [Presentation] 中心グラフの支配数に着目したグラフの分類について2022

    • Author(s)
      藤田慎也
    • Organizer
      日本数学会2022年度秋季総合分科会
    • Related Report
      2022 Research-status Report
  • [Presentation] 三角形を含まない高連結グラフにおける非分離パスの存在について2022

    • Author(s)
      藤田慎也
    • Organizer
      2022年度応用数学合同研究集会
    • Related Report
      2022 Research-status Report
  • [Presentation] New classification of graphs in view of the domination number of central graphs2022

    • Author(s)
      Shinya Fujita
    • Organizer
      The 6th Xi'an International Workshop on Graph Theory and Combinatorics
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] 辺着色グラフの rainbow connectivity に関する極値問題2022

    • Author(s)
      藤田慎也
    • Organizer
      2022年度日本数学会年会
    • Related Report
      2021 Research-status Report
  • [Presentation] グラフの安全集合に関する最近の結果と未解決問題について2021

    • Author(s)
      藤田慎也
    • Organizer
      2021年度日本数学会秋季総合分科会
    • Related Report
      2021 Research-status Report
  • [Presentation] 重み付きグラフ上の順序と頂点彩色に関する話題2021

    • Author(s)
      藤田慎也
    • Organizer
      離散数学とその応用研究集会2021
    • Related Report
      2021 Research-status Report
  • [Presentation] Some results on optimal proper connection number in edge-colored graphs2021

    • Author(s)
      Shinya Fujita
    • Organizer
      The 5th Xi'an International Workshop on Graph Theory and Combinatorics
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The optimal proper connection number of a graph with given independence number2021

    • Author(s)
      藤田慎也、Boram Park
    • Organizer
      2021年度日本数学会年会
    • Related Report
      2020 Research-status Report
  • [Presentation] Stable Structure on Safe Set Problems in Vertex-Weighted Graphs II -Recognition and Complexity-2020

    • Author(s)
      藤田慎也、Boram Park、佐久間雅
    • Organizer
      46th International Workshop, WG2020
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] On properly ordered coloring of vertices in a vertex-weighted graph2020

    • Author(s)
      藤田慎也、Sergey Kitaev、佐藤静佳、Li-Da Tong
    • Organizer
      2020年度日本数学会秋季総合分科会
    • Related Report
      2020 Research-status Report
  • [Presentation] グラフの optimal proper connection number に関する研究の進展2020

    • Author(s)
      藤田慎也
    • Organizer
      2020組合せ論とその周辺研究集会
    • Related Report
      2019 Research-status Report
  • [Presentation] Recent progress on safe set problems in vertex-weighted graphs2019

    • Author(s)
      Fujita Shinya
    • Organizer
      International Conference on Graph Theory and Combinatorics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Some recent results on safe set problems in vertex-weighted graphs2019

    • Author(s)
      Fujita Shinya
    • Organizer
      2019 Workshop on the Theory of Colored Graphs
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Safe sets in digraphs2019

    • Author(s)
      Bai Yandong, Bang-Jensen Joergen, Fujita Shinya, Yeo Anders
    • Organizer
      応用数学合同研究集会
    • Related Report
      2019 Research-status Report
  • [Presentation] Stable networks and connected safe set problem2019

    • Author(s)
      藤田慎也, Boram Park, 佐久間雅
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2019 Research-status Report

URL: 

Published: 2019-04-18   Modified: 2025-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi