Induced Ramsey-type theorems

• Autores: Jacob Fox, Benny Sudakov
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 6, 2008, págs. 1771-1801
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.07.009
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• Resumen

  • 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, Erdos�Hajnal, Prömel�Rödl, Nikiforov, Chung�Graham, and Luczak�Rödl. The proofs are based on a simple lemma (generalizing one by Graham, Rödl, and Rucinski) 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