The 3-colour Ramsey number of a 3-uniform berge cycle

András Gyárfás, Gábor N. Sárközy

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The asymptotics of 2-colour Ramsey numbers of loose and tight cycles in 3-uniform hypergraphs were recently determined [16, 17]. We address the same problem for Berge cycles and for 3 colours. Our main result is that the 3-colour Ramsey number of a 3-uniform Berge cycle of length n is asymptotic to 5n/4. The result is proved with the Regularity Lemma via the existence of a monochromatic connected matching covering asymptotically 4n/5 vertices in the multicoloured 2-shadow graph induced by the colouring of Kn(3).

Original languageEnglish
Pages (from-to)53-71
Number of pages19
JournalCombinatorics Probability and Computing
Volume20
Issue number1
DOIs
Publication statusPublished - Jan 1 2011

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics

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