Edge disjoint Hamilton cycles in random digraphs of constant minimum degree
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918443346821120 |
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| author | Cooper, Colin Frieze, Alan |
| author_facet | Cooper, Colin Frieze, Alan |
| contents | We study the existence of directed Hamilton cycles in random digraphs with $m$ edges where we condition on minimum in- and out-degree $\d \ge k+1$, where $k \ge 1$. Denote such a random graph by $D_{n,m}^{(δ\geq k+1)}$. Let $m=cn$ and $c\ge c_k$, where $c_k$ is a sufficiently large constant. We prove that w.h.p. $D_{n,m}^{(δ\geq k+1)}$ contains $k$ edge disjoint Hamilton cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11633 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Edge disjoint Hamilton cycles in random digraphs of constant minimum degree Cooper, Colin Frieze, Alan Combinatorics We study the existence of directed Hamilton cycles in random digraphs with $m$ edges where we condition on minimum in- and out-degree $\d \ge k+1$, where $k \ge 1$. Denote such a random graph by $D_{n,m}^{(δ\geq k+1)}$. Let $m=cn$ and $c\ge c_k$, where $c_k$ is a sufficiently large constant. We prove that w.h.p. $D_{n,m}^{(δ\geq k+1)}$ contains $k$ edge disjoint Hamilton cycles. |
| title | Edge disjoint Hamilton cycles in random digraphs of constant minimum degree |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.11633 |