| 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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| 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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