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arXiv · 2502.09830

Unavoidable subgraphs in Ramsey graphs

Christian Reiher·Vojtěch Rödl·Mathias Schacht
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Abstract

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.

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Christian Reiher, Vojtěch Rödl, Mathias Schacht. 2025-02-14. Unavoidable subgraphs in Ramsey graphs. https://arxiv.org/abs/2502.09830

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