3-Uniform hypergraphs of bounded degree have linear Ramsey numbers
Combinatorics
2007-05-23 v1
Abstract
Chv\'atal, R\"odl, Szemer\'edi 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.
Keywords
Cite
@article{arxiv.math/0608442,
title = {3-Uniform hypergraphs of bounded degree have linear Ramsey numbers},
author = {Oliver Cooley and Nikolaos Fountoulakis and Daniela Kühn and Deryk Osthus},
journal= {arXiv preprint arXiv:math/0608442},
year = {2007}
}
Comments
19 pages, 1 figure, submitted to J. Comb. Theory Ser. B