Hamiltonicity of graphs and its complexity
| Project/Area Number |
17K00018
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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 |
Theory of informatics
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| Research Institution | Nihon University |
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Principal Investigator |
SAITO Akira 日本大学, 文理学部, 教授 (90186924)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | ハミルトンサイクル / 計算量 / 2-因子 / マッチング / 辺着色 / Gallai着色 / ２部グラフ / 最小次数 / 弦 / 離散数学 / グラフ理論 |
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| Outline of Final Research Achievements |
A hamiltonian cycle in a graph G is a cycle which contains every vertex of G. A hamiltonian graph is a graph which contains a hamiltonian cycle. Many sufficient conditions for hamiltonicity have been obtained and a number of generalizations of hamiltonicity have been proposed in graph theory. We have reviewed them from the viewpoint of complexity.
In this research, we have put a particular focus on toughness and the binding number. Many graph theorists believe that their behaviors to hamiltonicity are similar. However, we have revealed that their effects on matchings in graphs are completely different, which strongly suggests that their behaviors to hamiltonicity also differ. We have also obtained a number of new insights into the relationship between matchings and planarity, k-trails and the distribution of chords in a cycle. Moreover, we have characterized the pairs and the triples of forbidden subgraphs that force the existence of a 2-factor in graphs.
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| Academic Significance and Societal Importance of the Research Achievements |
ハミルトンサイクルはグラフ理論における重要なテーマであると同時に、土木計画、交通計画、巡回セールスマン問題などの応用にも密接に関わる。一方その存在・非存在の決定はNP-完全であり、極めて困難な問題である。本研究はこれまでグラフ理論で得られてきたハミルトンサイクル存在のための十分条件やハミルトンサイクルの拡張概念に計算量の立場から光を当て、その困難さがどこに潜むのかを探った。得られた研究成果はハミルトン性の難しさの源に対する知見を与えると同時に、上記の応用分野に１つの指針を与えることになる。
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Report
(4 results)
Research Products
(24 results)
