The Ramsey number of the clique and the hypercube
Abstract
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 Erdos 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 ∈ and every sufficiently large n ∈ .
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