The generalizations of Hamiltonian in oriented graphs
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929235188252672 |
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| author | Zhou, Jia Wang, Zhilan Yan, Jin |
| author_facet | Zhou, Jia Wang, Zhilan Yan, Jin |
| contents | An oriented graph is an orientation of a simple graph. In 2009, Keevash, Kühn and Osthus proved that every sufficiently large oriented graph $D$ of order $n$ with $(3n-4)/8$ is Hamiltonian. Later, Kelly, Kühn and Osthus showed that it is also pancyclic. Inspired by this, we show that for any given constant $t$ and positive integer partition $n = n_1 + \cdots + n_t$, if $D$ is an oriented graph on $n$ vertices with minimum semidegree at least $(3n-4)/8$, then it contains $t$ disjoint cycles of lengths $n_1,\ldots , n_t$. Also, we determine the bounds on the semidegree of sufficiently large oriented graphs that are strongly Hamiltonian-connected, $k$-ordered Hamiltonian and spanning $k$-linked. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03878 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The generalizations of Hamiltonian in oriented graphs Zhou, Jia Wang, Zhilan Yan, Jin Combinatorics 05C20, 05C38, 05C70 An oriented graph is an orientation of a simple graph. In 2009, Keevash, Kühn and Osthus proved that every sufficiently large oriented graph $D$ of order $n$ with $(3n-4)/8$ is Hamiltonian. Later, Kelly, Kühn and Osthus showed that it is also pancyclic. Inspired by this, we show that for any given constant $t$ and positive integer partition $n = n_1 + \cdots + n_t$, if $D$ is an oriented graph on $n$ vertices with minimum semidegree at least $(3n-4)/8$, then it contains $t$ disjoint cycles of lengths $n_1,\ldots , n_t$. Also, we determine the bounds on the semidegree of sufficiently large oriented graphs that are strongly Hamiltonian-connected, $k$-ordered Hamiltonian and spanning $k$-linked. |
| title | The generalizations of Hamiltonian in oriented graphs |
| topic | Combinatorics 05C20, 05C38, 05C70 |
| url | https://arxiv.org/abs/2402.03878 |