Ramsey numbers for tournaments

Yannis Manoussakis, Zsolt Tuza

Research output: Contribution to journalArticle

Abstract

The Ramsey number r(D1,...,Dk) of acyclic directed graphs D1,...,Dk is defined as the largest integer r for which there exists a tournament T = (V,A) on r vertices with a k-coloring φ:A → {1,...,k} of the arc set A such that no Di occurs in color i for any i ∈ {1,...,k}. We discuss recursive techniques to compute r(D1,...,Dk) in the case where there are paths and/or stars among the Di. In particular, solving a problem of Bialostocki and Dierker [Congr. Numer. 47 (1985) 119-123], we prove that r(D1,D2)=r(D1)·r(D2) holds if D1 is transitive and D2 = Sn is an out-going star on n vertices. Our main result is an asymptotic formula for r(D1,...,Dk,Sn) where the digraphs D1,...,Dk are fixed arbitrarily and n → ∞.

Original languageEnglish
Pages (from-to)75-85
Number of pages11
JournalTheoretical Computer Science
Volume263
Issue number1-2
DOIs
Publication statusPublished - Aug 14 2001

Keywords

  • Ramsey number
  • Tournament

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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