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Characterizations of difference between forbidden subgraph conditions and the establishment of their methods

Research Project

Project/Area Number 18K13449
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 12030:Basic mathematics-related
Research InstitutionKitasato University

Principal Investigator

Furuya Michitaka  北里大学, 一般教育部, 准教授 (40711792)

Project Period (FY) 2018-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsグラフ理論 / 禁止部分グラフ / ラムゼー型問題 / 支配数 / 道被覆数 / 次数因子 / Gyarfas-Sumner予想 / 次数制約木 / 閉路被覆数 / 彩色数 / 内周 / ハミルトン閉路 / 禁止グラフ / Erdos-Hajnal予想
Outline of Final Research Achievements

In this research, our main aim is to make sure of essential effects given by forbidden subgraph conditions. To do so, we studied comparisons between forbidden subgraph conditions and relationship between forbidden subgraphs and various graph-invariants. As a result, Ramsey-type problems for graph-invariants were established. The problem is strongly related to the classical Gyarfas-Sumner conjecture, and the solution of its analogues from the point of view of Ramsey-type problem provides a new research direction for the conjecture. By reviewing the properties of forbidden subgraph conditions, we also gave a common generalization of known results concerning the existence of Hamiltonian cycle. Furthermore, inspired by such studies, we unify well-known domination-like invariants. Applying them, some results on domination number were analyzed in detail.

Academic Significance and Societal Importance of the Research Achievements

禁止グラフ条件は,グラフの構造や不変量を研究する際に頻繁に用いられる重要な十分条件である.しかしそれらの条件自体がグラフに与える本質的な影響や,複数の禁止グラフ条件間の性質比較という基礎研究はほとんど注目されていなかった.本研究ではそれを補う研究を進めたことによって,既存成果の整理や一般化を行うことに成功した.これらの結果により,禁止グラフ条件を用いる研究全域の進展に繋がったと言える.

Report

(7 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
  • 2018 Research-status Report
  • Research Products

    (36 results)

All 2023 2022 2021 2020 2019 2018 Other

All Int'l Joint Research (3 results) Journal Article (19 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 19 results,  Open Access: 5 results) Presentation (12 results) (of which Int'l Joint Research: 2 results,  Invited: 3 results) Remarks (2 results)

  • [Int'l Joint Research] Georgia State University/Illinois State University(米国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Hankuk University of Foreign Studies/KAIST/Ajou University(韓国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Georgia Southern University(米国)

    • Related Report
      2018 Research-status Report
  • [Journal Article] Ramsey-type results for path covers and path partitions. II. digraphs2023

    • Author(s)
      Shuya Chiba, Michitaka Furuya
    • Journal Title

      Applied Mathematics and Computation

      Volume: 458 Pages: 128205-128205

    • DOI

      10.1016/j.amc.2023.128205

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Factors with Red-Blue Coloring of Claw-Free Graphs and Cubic Graphs2023

    • Author(s)
      Furuya Michitaka、Kano Mikio
    • Journal Title

      Graphs and Combinatorics

      Volume: 39 Issue: 4

    • DOI

      10.1007/s00373-023-02680-6

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Degree sum condition for the existence of spanning k-trees in star-free graphs2022

    • Author(s)
      M. Furuya, S. Maezawa, R. Matsubara, H. Matsuda, S. Tsuchiya, T. Yashima
    • Journal Title

      Discussiones Mathematicae Graph Theory

      Volume: 42 Pages: 5-13

    • DOI

      10.7151/dmgt.2234

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Small domination-type invariants in random graphs2022

    • Author(s)
      Furuya Michitaka、Kawasaki Tamae
    • Journal Title

      Journal of Combinatorics

      Volume: 13 Issue: 4 Pages: 531-543

    • DOI

      10.4310/joc.2022.v13.n4.a4

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Forbidden triples generating a finite set of graphs with minimum degree three2022

    • Author(s)
      Egawa Yoshimi、Furuya Michitaka
    • Journal Title

      Discrete Applied Mathematics

      Volume: 320 Pages: 282-295

    • DOI

      10.1016/j.dam.2022.05.001

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Ramsey-Type Results for Path Covers and Path Partitions2022

    • Author(s)
      Shuya Chiba, Michitaka Furuya
    • Journal Title

      The Electronic Journal of Combinatorics

      Volume: 29 Issue: 4

    • DOI

      10.37236/10639

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Factors of bi-regular bipartite graphs2022

    • Author(s)
      Egawa Yoshimi、Furuya Michitaka、Kano Mikio
    • Journal Title

      Discrete Applied Mathematics

      Volume: 322 Pages: 268-272

    • DOI

      10.1016/j.dam.2022.08.016

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] A characterization of 2-connected {K1,3,N3,1,1}-free non-Hamiltonian graphs2021

    • Author(s)
      Shuya Chiba, Michitaka Furuya
    • Journal Title

      Discrete Mathematics

      Volume: 344 Issue: 5 Pages: 112321-112321

    • DOI

      10.1016/j.disc.2021.112321

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] A continuous generalization of domination-like invariants2021

    • Author(s)
      Furuya Michitaka
    • Journal Title

      Journal of Combinatorial Optimization

      Volume: 41 Issue: 4 Pages: 905-922

    • DOI

      10.1007/s10878-021-00725-1

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] A characterization of trees based on edge-deletion and its applications for domination-type invariants2021

    • Author(s)
      Furuya Michitaka
    • Journal Title

      Discrete Applied Mathematics

      Volume: 299 Pages: 50-61

    • DOI

      10.1016/j.dam.2021.04.020

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Existence of a spanning tree having small diameter2021

    • Author(s)
      Egawa Yoshimi、Furuya Michitaka、Matsumura Hajime
    • Journal Title

      Discrete Mathematics

      Volume: 344 Issue: 11 Pages: 112548-112548

    • DOI

      10.1016/j.disc.2021.112548

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Long Paths in Bipartite Graphs and Path-Bistar Bipartite Ramsey Numbers2020

    • Author(s)
      Michitaka Furuya, Shunichi Maezawa, Kenta Ozeki
    • Journal Title

      Graphs and Combinatorics

      Volume: 36 Issue: 1 Pages: 167-176

    • DOI

      10.1007/s00373-019-02127-x

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Large homeomorphically irreducible trees in path-free graphs2020

    • Author(s)
      M. Furuya, and S. Tsuchiya
    • Journal Title

      Journal of Graph Theory

      Volume: 93 Issue: 3 Pages: 372-394

    • DOI

      10.1002/jgt.22492

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Ramsey-type theorem for the matching number regarding connected graphs2020

    • Author(s)
      Choi Ilkyoo、Furuya Michitaka、Kim Ringi、Park Boram
    • Journal Title

      Discrete Mathematics

      Volume: 343 Issue: 2 Pages: 111648-111648

    • DOI

      10.1016/j.disc.2019.111648

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A degree sum condition on the order, the connectivity and the independence number for Hamiltonicity2019

    • Author(s)
      S.Chiba, M.Furuya, K.Ozeki, M.Tsugaki and T.Yamashita
    • Journal Title

      Electronic Journal of Combinatorics

      Volume: 26 Issue: 4

    • DOI

      10.37236/5480

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Characterizing the Difference Between Graph Classes Defined by Forbidden Pairs Including the Claw2019

    • Author(s)
      Chen Guantao、Furuya Michitaka、Shan Songling、Tsuchiya Shoichi、Yang Ping
    • Journal Title

      Graphs and Combinatorics

      Volume: 35 Issue: 6 Pages: 1459-1474

    • DOI

      10.1007/s00373-019-02108-0

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A note on domination 3-edge-critical planar graphs2019

    • Author(s)
      Michitaka Furuya, Naoki Matsumoto
    • Journal Title

      Information Processing Letters

      Volume: 142 Pages: 64-67

    • DOI

      10.1016/j.ipl.2018.10.014

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [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
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Forbidden subgraphs for constant domination number2018

    • Author(s)
      Michitaka Furuya
    • Journal Title

      Discrete Mathematics and Theoretical Computer Science

      Volume: 20

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] HIST的全域木の構成と禁止グラフ2023

    • Author(s)
      古谷 倫貴、土屋 翔一
    • Organizer
      Japanese Conference on Combinatorics and its Applications 2023・離散数学とその応用研究集会2023
    • Related Report
      2023 Annual Research Report
  • [Presentation] 次数積条件とグラフの連結性2023

    • Author(s)
      古谷倫貴
    • Organizer
      2022年度RIMS共同研究「グラフの辺着色グラフへの拡張性および非拡張性」
    • Related Report
      2022 Research-status Report
  • [Presentation] Ramsey型問題からのGyarfas-Sumner予想へのアプローチ2022

    • Author(s)
      古谷倫貴、千葉周也
    • Organizer
      Japanese Conference on Combinatorics and its Applications 2022・離散数学とその応用研究集会2022
    • Related Report
      2022 Research-status Report
  • [Presentation] cover/partition numberに見る不変量版ラムゼー問題2021

    • Author(s)
      古谷倫貴、千葉周也
    • Organizer
      2021年度応用数学合同研究集会
    • Related Report
      2021 Research-status Report
  • [Presentation] グラフクラスの有限性と禁止部分グラフ条件2020

    • Author(s)
      古谷倫貴
    • Organizer
      日本応用数理学会2020年度年会
    • Related Report
      2020 Research-status Report
  • [Presentation] 禁止部分グラフによる十分条件の決定の難易2020

    • Author(s)
      古谷倫貴
    • Organizer
      2020組合せ論とその周辺研究集会
    • Related Report
      2019 Research-status Report
  • [Presentation] Bounds on self domination number and an edge-deletion operation in trees2020

    • Author(s)
      古谷倫貴
    • Organizer
      日本数学会2020年度年会
    • Related Report
      2019 Research-status Report
  • [Presentation] グラフのテンソル積の染色数とグレブナー基底2020

    • Author(s)
      深作亮也,古谷倫貴,東谷章弘
    • Organizer
      日本数学会2020年度年会
    • Related Report
      2019 Research-status Report
  • [Presentation] Self domination in random graphs2019

    • Author(s)
      古谷倫貴,川崎玉恵
    • Organizer
      2019年度応用数学合同研究集会
    • Related Report
      2019 Research-status Report
  • [Presentation] 局所構造条件を満たすグラフの集合の 比較と特徴付け2019

    • Author(s)
      古谷倫貴
    • Organizer
      日本数学会
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] A continuous generalization of domination-type invariants2018

    • Author(s)
      Michitaka Furuya
    • Organizer
      The Fourth Japan-Sino Symposium on Graph Theory, Combinatorics and Their Applications
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Difference between forbidden subgraph conditions2018

    • Author(s)
      Michitaka Furuya
    • Organizer
      2018 SCMS Workshop on Extremal and Structural Graph Theory
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Remarks] Michitaka Furuya's homepage

    • URL

      https://sites.google.com/site/michitakafuruya/

    • Related Report
      2023 Annual Research Report 2022 Research-status Report 2021 Research-status Report
  • [Remarks] Michitaka Furuya's homepage

    • URL

      https://sites.google.com/site/michitakafuruya

    • Related Report
      2020 Research-status Report

URL: 

Published: 2018-04-23   Modified: 2025-01-30  

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