The Ramsey number of the clique and the hypercube
Combinatorics
2017-05-17 v1
Abstract
The Ramsey number r(K_s,Q_n) is the smallest positive integer N such that every red-blue colouring of the edges of the complete graph K_N on N vertices contains either a red n-dimensional hypercube, or a blue clique on s vertices. Answering a question of Burr and Erd\H{o}s from 1983, and improving on recent results of Conlon, Fox, Lee and Sudakov, and of the current authors, we show that r(K_s,Q_n) = (s-1) (2^n - 1) + 1 for every s \in \N and every sufficiently large n \in \N.
Cite
@article{arxiv.1306.0461,
title = {The Ramsey number of the clique and the hypercube},
author = {Gonzalo Fiz Pontiveros and Simon Griffiths and Robert Morris and David Saxton and Jozef Skokan},
journal= {arXiv preprint arXiv:1306.0461},
year = {2017}
}
Comments
27 pages