Year: 2007
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Fox, Jacob, Sudakov, Benny
Institutions: Princeton University, University of California, Los Angeles
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951969930