2022 Fiscal Year Final Research Report
A study on the relation of degree conditions for the existence of substructures in graphs
| Project/Area Number |
16K05262
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kindai University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2023-03-31
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| Keywords | 閉路 / 次数条件 |
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| Outline of Final Research Achievements |
Chiba and I wrote a survey paper on degree conditions for the existence of a specified number of cycles or paths in a graph. In the process, we obtained three results on degree-sum conditions for partitioning a graph into cycles. With Chen, Chiba, Gould, Gu, Saito, and Tsugaki, I proved that dense graphs have dense bipartite graphs as substructures in terms of degree sums of non-adjacent two-vertices. In work with Ota and Chiba, I obtained a result that is a common generalization of Bondy and Vince's conjecture on the distribution of cycle lengths (in 1998) and a conjecture by Ma et al. (in 2018).
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| Free Research Field |
グラフ理論
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| Academic Significance and Societal Importance of the Research Achievements |
小関氏との共著である2008年の論文で，ハミルトン閉路が存在するための次数和条件に関して，その最良の下限は公差が「独立数－1」の等差数列をなすという予想をした．津垣氏，小関氏，千葉氏，古谷氏と共同研究で，未解決であったこの予想を解決し，2019年に論文として掲載された．千葉氏と執筆した，指定された個数の閉路または道がグラフに存在するための次数条件についてのサーヴェイ論文は，2018年1月に国際雑誌に掲載され，2023年5月現在1259回アクセスされていて，11本の論文で引用されている．
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