Unavoidable subgraphs in Ramsey graphs
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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