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The girth Ramsey theorem
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abstract
Given a hypergraph $F$ and a number of colours $r$, there exists a hypergraph $H$ of the same girth satisfying $H\longrightarrow (F)_r$. Moreover, for every linear hypergraph $F$ there exists a Ramsey hypergraph $H$ that locally looks like a forest of copies of $F$.
Forward citations
Cited by 2 Pith papers
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Off-Diagonal Ramsey Numbers for Linear Hypergraphs
For every k≥4 and C>1 there is a linear k-uniform hypergraph H with off-diagonal Ramsey number r(H,K_n^{(k)}) at least the (k-2)-fold tower of 2^{(log n)^C}.
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Unavoidable subgraphs in Ramsey graphs
For cycles and balanced complete multipartite graphs, every forest of copies of F is forced in large Ramsey graphs, but infinitely many graphs F admit Ramsey graphs that avoid all non-trivial such forests.
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