Vertex-Disjoint Subtournaments of Prescribed Minimum Outdegree or Minimum Semidegree: Proof for Tournaments of a Conjecture of Stiebi

It was proved (Bessy et al., 2010) that for ≥1, a tournament with minimum semidegree at least 2？1 contains at least r vertex-disjoint directed triangles. It was also proved (Lichiardopol, 2010) that for integers ≥3 and ≥1, every tournament with minimum semidegree at least (？1)？1 contains at least r vertex-disjoint directed cycles of length . None information was given on these directed cycles. In this paper, we fill a little this gap. Namely, we prove that for ≥1 and ≥1, every tournament of minimum outdegree at least ((2