A Ramsey-type result for the hypercube

Noga Alon*, Radoš Radoičić, Benny Sudakov, Jan Vondrák

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We prove that for every fixed k and ℓ ≥ 5 and for sufficiently large n, every edge coloring of the hypercube Qn with k colors contains a monochromatic cycle of length 2ℓ. This answers an open question of Chung. Our techniques provide also a characterization of all subgraphs H of the hypercube which are Ramsey, that is, have the property that for every k, any k-edge coloring of a sufficiently large Qn contains a monochromatic copy of H.

Original languageEnglish
Pages (from-to)196-208
Number of pages13
JournalJournal of Graph Theory
Issue number3
StatePublished - Nov 2006


  • Hypercube
  • Monochromatic cycles
  • Ramsey theory


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