Induced Ramsey-type theorems
Combinatorics
2007-12-27 v3
Abstract
We present a unified approach to proving Ramsey-type theorems for graphs with a forbidden induced subgraph which can be used to extend and improve the earlier results of Rodl, Erdos-Hajnal, Promel-Rodl, Nikiforov, Chung-Graham, and Luczak-Rodl. The proofs are based on a simple lemma (generalizing one by Graham, Rodl, and Rucinski) that can be used as a replacement for Szemeredi's regularity lemma, thereby giving much better bounds. The same approach can be also used to show that pseudo-random graphs have strong induced Ramsey properties. This leads to explicit constructions for upper bounds on various induced Ramsey numbers.
Keywords
Cite
@article{arxiv.0706.4112,
title = {Induced Ramsey-type theorems},
author = {Jacob Fox and Benny Sudakov},
journal= {arXiv preprint arXiv:0706.4112},
year = {2007}
}