Thomassen's theorem on the two-linkage problem in acyclic digraphs: a shorter proof
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929500377317376 |
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| author | Seymour, Paul |
| author_facet | Seymour, Paul |
| contents | Let G be an acyclic digraph, and let a, b, c, d be vertices, where a, b are sources, c, d are sinks, and every other vertex has in-degree and out-degree at least two. In 1985, Thomassen showed that there do not exist disjoint directed paths from a to c and from b to d, if and only if G can be drawn in a closed disc with a, b, c, d drawn in the boundary in order. We give a shorter proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09758 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Thomassen's theorem on the two-linkage problem in acyclic digraphs: a shorter proof Seymour, Paul Combinatorics 05C10 Let G be an acyclic digraph, and let a, b, c, d be vertices, where a, b are sources, c, d are sinks, and every other vertex has in-degree and out-degree at least two. In 1985, Thomassen showed that there do not exist disjoint directed paths from a to c and from b to d, if and only if G can be drawn in a closed disc with a, b, c, d drawn in the boundary in order. We give a shorter proof. |
| title | Thomassen's theorem on the two-linkage problem in acyclic digraphs: a shorter proof |
| topic | Combinatorics 05C10 |
| url | https://arxiv.org/abs/2409.09758 |