The Ramsey number of the clique and the hypercube

Fiz Pontiveros, Gonzalo, Griffiths, Simon, Morris, Robert, Saxton, David and Skokan, Jozef ORCID: 0000-0003-3996-7676 (2014) The Ramsey number of the clique and the hypercube. Journal of the London Mathematical Society, 89 (3). 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
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	11 Jun 2014 15:43
Last Modified:	12 Dec 2024 00:38
Funders:	CNPq bolsas PDJ, CNPq bolsa de Produtividade em Pesquisa, Santander Travel Fund
URI:	http://eprints.lse.ac.uk/id/eprint/57071

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