Ramsey numbers of cubes versus cliques
Combinatorics
2013-12-16 v2
Abstract
The cube graph Q_n is the skeleton of the n-dimensional cube. It is an n-regular graph on 2^n vertices. The Ramsey number r(Q_n, K_s) is the minimum N such that every graph of order N contains the cube graph Q_n or an independent set of order s. Burr and Erdos in 1983 asked whether the simple lower bound r(Q_n, K_s) >= (s-1)(2^n - 1)+1 is tight for s fixed and n sufficiently large. We make progress on this problem, obtaining the first upper bound which is within a constant factor of the lower bound.
Keywords
Cite
@article{arxiv.1208.1732,
title = {Ramsey numbers of cubes versus cliques},
author = {David Conlon and Jacob Fox and Choongbum Lee and Benny Sudakov},
journal= {arXiv preprint arXiv:1208.1732},
year = {2013}
}
Comments
26 pages