2023 Fiscal Year Final Research Report
Characterizations of difference between forbidden subgraph conditions and the establishment of their methods
| Project/Area Number |
18K13449
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 12030:Basic mathematics-related
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| Research Institution | Kitasato University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2024-03-31
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| 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 |
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| 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.
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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 |
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．
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