Infinite grids in digraphs
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912927168069632 |
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| author | Hamann, Matthias Heuer, Karl |
| author_facet | Hamann, Matthias Heuer, Karl |
| contents | Halin proved that every graph with an end $ω$ containing infinitely many pairwise disjoint rays admits a subdivision of the infinite quarter-grid as a subgraph where all rays from that subgraph belong to $ω$. We will prove a corresponding statement for digraphs, that is, we will prove that every digraph that has an end with infinitely many pairwise disjoint directed rays contains a subdivision of a grid-like digraph all of whose directed rays belong to that end. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03302 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Infinite grids in digraphs Hamann, Matthias Heuer, Karl Combinatorics 05C63, 05C20 (primary), 05C38 (secondary) Halin proved that every graph with an end $ω$ containing infinitely many pairwise disjoint rays admits a subdivision of the infinite quarter-grid as a subgraph where all rays from that subgraph belong to $ω$. We will prove a corresponding statement for digraphs, that is, we will prove that every digraph that has an end with infinitely many pairwise disjoint directed rays contains a subdivision of a grid-like digraph all of whose directed rays belong to that end. |
| title | Infinite grids in digraphs |
| topic | Combinatorics 05C63, 05C20 (primary), 05C38 (secondary) |
| url | https://arxiv.org/abs/2412.03302 |