On the Ramsey number of the triangle and the cube

Pontiveros, Gonzalo Fiz, Griffiths, Simon, Morris, Robert, Saxton, David and Skokan, Jozef (2016) On the Ramsey number of the triangle and the cube. Combinatorica, 36 (1). pp. 71-89. ISSN 0209-9683

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Abstract

The Ramsey number r(K 3,Q n ) is the smallest integer N such that every red-blue colouring of the edges of the complete graph K N contains either a red n-dimensional hypercube, or a blue triangle. Almost thirty years ago, Burr and Erdős conjectured that r(K 3,Q n )=2 n+1−1 for every n∈ℕ, but the first non-trivial upper bound was obtained only recently, by Conlon, Fox, Lee and Sudakov, who proved that r(K 3,Q n )⩽7000·2 n . Here we show that r(K 3,Q n )=(1+o(1))2 n+1 as n→∞.

Item Type:	Article
Official URL:	http://link.springer.com/journal/493
Additional Information:	© 2015 Springer
Library of Congress subject classification:	Q Science > QA Mathematics
Sets:	Departments > Mathematics
Funders:	CNPq bolsas PDJ (GFP, SG, DS), CNPq bolsa de Produtividade em Pesquisa (RM)
Date Deposited:	17 Jun 2015 13:42
URL:	http://eprints.lse.ac.uk/62348/

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