Linear Ramsey numbers for bounded-degree hypergraphs

Abstract

We show that the Ramsey number is linear for every uniform hypergraph with bounded-degree. This is a hypergraph extension of the famous theorem for ordinary graphs which Chvátal et al. showed in 1983. Our proof is simple, contains the multicolor case, and provides a strong embedding lemma. It shows the potential of a new hypergraph regularity lemma by the author.

11 pages

References in corpus (4)

• A Simple Regularization of Hypergraphs
• Embeddings and Ramsey numbers of sparse k-uniform hypergraphs
• Removal lemma for infinitely-many forbidden hypergraphs and property testing
• 3-Uniform hypergraphs of bounded degree have linear Ramsey numbers

Cited by in corpus (4)

• A Simple Regularization of Hypergraphs
• The number of hypergraphs and colored Hypergraphs with hereditary properties
• Removal lemma for infinitely-many forbidden hypergraphs and property testing
• A simple regularization of graphs