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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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Identification Number: 10.1112/jlms/jdu004


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:
Additional Information: © 2014 London Mathematical Society
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 11 Jun 2014 15:43
Last Modified: 20 Oct 2021 02:10
Funders: CNPq bolsas PDJ, CNPq bolsa de Produtividade em Pesquisa, Santander Travel Fund

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