Unavoidable subgraphs in Ramsey graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909493120466944 |
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| author | Reiher, Christian Rödl, Vojtěch Schacht, Mathias |
| author_facet | Reiher, Christian Rödl, Vojtěch Schacht, Mathias |
| contents | We study subgraphs that appear in large Ramsey graphs for a given graph $F$. The recent girth Ramsey theorem of the first two authors asserts that there are Ramsey graphs such that all small subgraphs are `forests of copies of $F$' amalgamated on vertices and edges. We derive a few further consequences from this structural result and investigate to which extent such forests of copies must be present in Ramsey graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09830 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unavoidable subgraphs in Ramsey graphs Reiher, Christian Rödl, Vojtěch Schacht, Mathias Combinatorics 05D10, 05C55 We study subgraphs that appear in large Ramsey graphs for a given graph $F$. The recent girth Ramsey theorem of the first two authors asserts that there are Ramsey graphs such that all small subgraphs are `forests of copies of $F$' amalgamated on vertices and edges. We derive a few further consequences from this structural result and investigate to which extent such forests of copies must be present in Ramsey graphs. |
| title | Unavoidable subgraphs in Ramsey graphs |
| topic | Combinatorics 05D10, 05C55 |
| url | https://arxiv.org/abs/2502.09830 |