The Ramsey number of the clique and the hypercube

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 Erdős from 1983, and improving on recen...

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Veröffentlicht in:	Journal of the London Mathematical Society 2014-06, Vol.89 (3), p.680-702
Hauptverfasser:	Fiz Pontiveros, Gonzalo, Griffiths, Simon, Morris, Robert, Saxton, David, Skokan, Jozef
Format:	Artikel
Sprache:	eng
Schlagworte:	Burrs Colouring Graphs Hypercubes Integers Mathematical analysis
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description	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 Erdős 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∈N and every sufficiently large n∈N.
doi_str_mv	10.1112/jlms/jdu004
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subjects	Burrs Colouring Graphs Hypercubes Integers Mathematical analysis
title	The Ramsey number of the clique and the hypercube
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