Domination in tournaments Academic Article uri icon


  • 2017 Elsevier Inc. 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.

published proceedings

  • Journal of Combinatorial Theory Series B

author list (cited authors)

  • Chudnovsky, M., Kim, R., Liu, C., Seymour, P., & Thomass, S.

citation count

  • 4

complete list of authors

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

publication date

  • January 2018