Hamilton cycles in random digraphs with minimum degree at least one
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915344150429696 |
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| author | Cooper, Colin Frieze, Alan |
| author_facet | Cooper, Colin Frieze, Alan |
| contents | We study the existence of a directed Hamilton cycle in random digraphs with $m$ edges where we condition on minimum in- and out-degree at least one. Denote such a random graph by $D_{n,m}^{(δ\geq1)}$. We prove that if $m=\tfrac n2(\log n+2\log\log n+c_n)$ then \[ \lim_{n\to\infty}\Pr(D_{n,m}^{(δ\geq1)}\text{ is Hamiltonian})=\begin{cases}0&c_n\to-\infty.\\e^{-e^{-c}/4}&c_n\to c.\\1&c_n\to\infty.\end{cases} \] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06781 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hamilton cycles in random digraphs with minimum degree at least one Cooper, Colin Frieze, Alan Combinatorics We study the existence of a directed Hamilton cycle in random digraphs with $m$ edges where we condition on minimum in- and out-degree at least one. Denote such a random graph by $D_{n,m}^{(δ\geq1)}$. We prove that if $m=\tfrac n2(\log n+2\log\log n+c_n)$ then \[ \lim_{n\to\infty}\Pr(D_{n,m}^{(δ\geq1)}\text{ is Hamiltonian})=\begin{cases}0&c_n\to-\infty.\\e^{-e^{-c}/4}&c_n\to c.\\1&c_n\to\infty.\end{cases} \] |
| title | Hamilton cycles in random digraphs with minimum degree at least one |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2312.06781 |