Domination in tournaments

Maria Chudnovsky, Ringi Kim, Chun Hung Liu, Paul Seymour, Stéphan Thomassé

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We investigate the following conjecture of Hehui Wu: for every tournament S, the class of S-free tournaments has bounded domination number. We show that the conjecture is false in general, but true when S is 2-colourable (that is, its vertex set can be partitioned into two transitive sets); the latter follows by a direct application of VC-dimension. Our goal is to go beyond this; we give a non-2-colourable tournament S that satisfies the conjecture. The key ingredient here (perhaps more interesting than the result itself) is that we overcome the unboundedness of the VC-dimension by showing that the set of shattered sets is sparse.

Original languageEnglish (US)
Pages (from-to)98-113
Number of pages16
JournalJournal of Combinatorial Theory. Series B
StatePublished - May 2018

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


  • Domination
  • Tournament
  • VC-dimension


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