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arXiv · 0706.4112

Induced Ramsey-type theorems

Jacob Fox·Benny Sudakov
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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.

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Jacob Fox, Benny Sudakov. 2007-12-27. Induced Ramsey-type theorems. https://arxiv.org/abs/0706.4112

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