The girth Ramsey theorem

Christian Reiher; Vojtěch Rödl

The girth Ramsey theorem

Combinatorics 2023-08-31 v1

Authors: Christian Reiher , Vojtěch Rödl

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 $F$ .

Keywords

ramsey numbers ramsey theory hypergraph theory

Cite

@article{arxiv.2308.15589,
  title  = {The girth Ramsey theorem},
  author = {Christian Reiher and Vojtěch Rödl},
  journal= {arXiv preprint arXiv:2308.15589},
  year   = {2023}
}

Comments

27 beautiful figures

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