Linear Ramsey numbers for bounded-degree hypergraphs

Details Linear Ramsey numbers for bounded-degree hypergraphs Linear Ramsey numbers for bounded-degree hypergraphs

2006-12-20

arxiv.org/abs/math/0612601v2

Mathematics

Combinatorics

11 pages

Scientific paper

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 Chv\'atal 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.

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