The Ramsey number of the clique and the hypercube

Fiz Pontiveros, Gonzalo, Griffiths, Simon, Morris, Robert, Saxton, David and Skokan, Jozef (2014) The Ramsey number of the clique and the hypercube. Journal of the London Mathematical Society, 89 (3). pp. 680-702. ISSN 0024-6107

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Abstract

The Ramsey number r(Ks,Qn) is the smallest positive integer N such that every red–blue colouring of the edges of the complete graph KN on N vertices contains either a red n-dimensional hypercube, or a blue clique on s vertices. Answering a question of Burr and Erdős from 1983, and improving on recent results of Conlon, Fox, Lee and Sudakov, and of the current authors, we show that r(Ks,Qn)=(s−1)(2n−1)+1 for every s∈N and every sufficiently large n∈N.

Item Type:	Article
Official URL:	http://jlms.oxfordjournals.org/
Additional Information:	© 2014 London Mathematical Society
Library of Congress subject classification:	Q Science > QA Mathematics
Sets:	Departments > Mathematics
Funders:	CNPq bolsas PDJ, CNPq bolsa de Produtividade em Pesquisa, Santander Travel Fund
Date Deposited:	11 Jun 2014 15:43
URL:	http://eprints.lse.ac.uk/57071/

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