Unavoidable subgraphs in Ramsey graphs
arXiv:2502.09830
Abstract
We study subgraphs that appear in large Ramsey graphs for a given graph . 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 ' 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.
18 pages