Decomposing oriented graphs into transitive tournaments

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For an oriented graph G with n vertices, let f(G) denote the minimum number of transitive subtournaments that decompose G. We prove several results on f(G). In particular, if G is a tournament then f(G)<521n2(1+o(1)) and there are tournaments for which f(G)>n2/3000. For general G we prove that f(G)≤⌊n2/3⌋ and this is tight. Some related parameters are also considered.

Original languageEnglish
Pages (from-to)166-170
Number of pages5
JournalDiscrete Mathematics
Issue number1
StatePublished - 28 Jan 2006


  • Decomposition
  • Tournament
  • Transitive

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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