Packing edge-disjoint triangles in regular and almost regular tournaments

Islam Akaria, Raphael Yuster

Research output: Contribution to journalArticlepeer-review


For a tournament T, let ν3(T) denote the maximum number of pairwise edge-disjoint triangles (directed cycles of length 3) in T. Let ν3(n) denote the minimum of ν3(T) ranging over all regular tournaments with n vertices (n odd). We conjecture that ν3(n)=(1+o(1))n2/9 and prove thatn211.43(1-o(1))≤ν3(n)≤n29(1+o(1)) improving upon the best known upper bound of n2-18 and lower bound of n211.5(1-o(1)). The result is generalized to tournaments where the indegree and outdegree at each vertex may differ by at most βn.

Original languageAmerican English
Pages (from-to)217-228
Number of pages12
JournalDiscrete Mathematics
Issue number2
StatePublished - 6 Feb 2015


  • Fractional
  • Packing
  • Tournament

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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