Hamiltonian cycles in $ 15 $-tough ($ P_{3}\cup 3P_{1} $)-free graphs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912461524828160 |
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| author | Ma, Hui Hao, Lili Yang, Weihua |
| author_facet | Ma, Hui Hao, Lili Yang, Weihua |
| contents | A graph $ G $ is called $ t $-tough if $ \left|S\right|\geq t\cdot w\left(G-S\right)$ for every cutset $ S $ of $G$. Chvátal conjectured that there exists a constant $ t_{0} $ such that every $ t_{0} $-tough graph has a hamiltonian cycle. Gao and Shan have proved that every $7$-tough $(P_{3}\cup 2P_{1})$-free grah is hamiltonian. In this paper, we confirm this conjecture for $ (P_{3}\cup 3P_{1}) $-free graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04189 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamiltonian cycles in $ 15 $-tough ($ P_{3}\cup 3P_{1} $)-free graphs Ma, Hui Hao, Lili Yang, Weihua Combinatorics A graph $ G $ is called $ t $-tough if $ \left|S\right|\geq t\cdot w\left(G-S\right)$ for every cutset $ S $ of $G$. Chvátal conjectured that there exists a constant $ t_{0} $ such that every $ t_{0} $-tough graph has a hamiltonian cycle. Gao and Shan have proved that every $7$-tough $(P_{3}\cup 2P_{1})$-free grah is hamiltonian. In this paper, we confirm this conjecture for $ (P_{3}\cup 3P_{1}) $-free graphs. |
| title | Hamiltonian cycles in $ 15 $-tough ($ P_{3}\cup 3P_{1} $)-free graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2505.04189 |