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. 7189.
ISSN 02099683
Abstract
The Ramsey number r(K 3,Q n ) is the smallest integer N such that every redblue colouring of the edges of the complete graph K N contains either a red ndimensional 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 nontrivial 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→∞.
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