Induced Ramsey-type theorems |
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Authors: | Jacob Fox Benny Sudakov |
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Affiliation: | a Department of Mathematics, Princeton University, Princeton, NJ, USA b Department of Mathematics, UCLA, Los Angeles, 90095, USA |
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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 Rödl, Erd?s-Hajnal, Prömel-Rödl, Nikiforov, Chung-Graham, and ?uczak-Rödl. The proofs are based on a simple lemma (generalizing one by Graham, Rödl, and Ruciński) that can be used as a replacement for Szemerédi'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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Keywords: | Ramsey numbers Quasirandom graphs Induced subgraphs |
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