Linear Ramsey numbers for bounded-degree hypergraphs
Combinatorics
2007-12-14 v2 Probability
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 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.
Keywords
Cite
@article{arxiv.math/0612601,
title = {Linear Ramsey numbers for bounded-degree hypergraphs},
author = {Yoshiyasu Ishigami},
journal= {arXiv preprint arXiv:math/0612601},
year = {2007}
}
Comments
11 pages