Packing edge-disjoint triangles in regular and almost regular tournaments

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Abstract

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 languageEnglish
Pages (from-to)217-228
Number of pages12
JournalDiscrete Mathematics
Volume338
Issue number2
DOIs
StatePublished - 6 Feb 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier B.V. All rights reserved.

Keywords

  • Fractional
  • Packing
  • Tournament

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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