On the Ramsey number of the triangle and the cube
Pontiveros, G. F., Griffiths, S., Morris, R., Saxton, D. & Skokan, J.
(2016).
On the Ramsey number of the triangle and the cube.
Combinatorica,
36(1), 71-89.
https://doi.org/10.1007/s00493-015-3089-8
(2016).
On the Ramsey number of the triangle and the cube.
Combinatorica,
36(1), 71-89.
https://doi.org/10.1007/s00493-015-3089-8
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→∞.