Ramsey Goodness and Beyond

Details Ramsey Goodness and Beyond Ramsey Goodness and Beyond

2007-03-21

arxiv.org/abs/math/0703653v2

Mathematics

Combinatorics

A new reference is added

Scientific paper

In a seminal paper from 1983, Burr and Erdos started the systematic study of Ramsey numbers of cliques vs. large sparse graphs, raising a number of problems. In this paper we develop a new approach to such Ramsey problems using a mix of the Szemeredi regularity lemma, embedding of sparse graphs, Turan type stability, and other structural results. We give exact Ramsey numbers for various classes of graphs, solving all but one of the Burr-Erdos problems.

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