On the Ramsey number of the triangle and the cube

Pontiveros, Gonzalo Fiz, Griffiths, Simon, Morris, Robert, Saxton, David and Skokan, Jozef ORCID: 0000-0003-3996-7676 (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
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	17 Jun 2015 13:42
Last Modified:	07 Jan 2024 08:48
Funders:	CNPq bolsas PDJ (GFP, SG, DS), CNPq bolsa de Produtividade em Pesquisa (RM)
URI:	http://eprints.lse.ac.uk/id/eprint/62348

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