A study for finding a new approach toward Ramsey-type problems in graphs
Project/Area Number |
15K04979
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Foundations of mathematics/Applied mathematics
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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)
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Project Period (FY) |
2015-04-01 – 2019-03-31
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Project Status |
Completed (Fiscal Year 2018)
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Budget Amount *help |
¥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)
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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.
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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.
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Report
(5 results)
Research Products
(36 results)
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[Journal Article] Safe set problem on graphs2016
Author(s)
Shinya Fujita, Gary MacGillivray, Tadashi Sakuma
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Journal Title
Discrete Applied Mathematics
Volume: 215
Pages: 106-111
DOI
Related Report
Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
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[Journal Article] From Edge-Coloring to Strong Edge-Coloring2015
Author(s)
Valentin Borozan, Gerard Jennhwa Chang, Nathann Cohen, Shinya Fujita, Narayanan Narayanan, Reza Naserasr, Petru Valicov
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Journal Title
Electronic Journal of Combinatorics
Volume: 22
Related Report
Peer Reviewed / Open Access / Int'l Joint Research
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[Presentation] Partitioning a graph into dense parts2016
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
Related Report
Int'l Joint Research / Invited
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