The Ramsey number of dense graphs
Combinatorics
2014-02-26 v1
Abstract
The Ramsey number r(H) of a graph H is the smallest number n such that, in any two-colouring of the edges of K_n, there is a monochromatic copy of H. We study the Ramsey number of graphs H with t vertices and density \r, proving that r(H) \leq 2^{c \sqrt{\r} \log (2/\r) t}. We also investigate some related problems, such as the Ramsey number of graphs with t vertices and maximum degree \r t and the Ramsey number of random graphs in \mathcal{G}(t, \r), that is, graphs on t vertices where each edge has been chosen independently with probability \r.
Keywords
Cite
@article{arxiv.0907.2657,
title = {The Ramsey number of dense graphs},
author = {David Conlon},
journal= {arXiv preprint arXiv:0907.2657},
year = {2014}
}
Comments
15 pages