vix.ing · top · new · best · stats · spec

3-Uniform hypergraphs of bounded degree have linear Ramsey numbers

2006/08/17 by Cooley, Oliver, Fountoulakis, Nikolaos, Kühn, Daniela +1
#05D10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0608442

Abstract

Chvátal, Rödl, Szemerédi and Trotter proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. We prove that the same holds for 3-uniform hypergraphs. The main new tool which we prove and use is an embedding lemma for 3-uniform hypergraphs of bounded maximum degree into suitable 3-uniform `pseudo-random' hypergraphs.

Related