Tiling transitive tournaments and their blow-ups

Research output: Contribution to journalArticlepeer-review


Let TTk denote the transitive tournament on k vertices. Let TT (h, k) denote the graph obtained from TTk by replacing each vertex with an independent set of size h ≥ 1. The following result is proved: Let c2 1/2, c3 = 5/6 and ck = 1 - 2 -k-logk for k ≥ 4. For every ε > 0 there exists N = N(ε, h, k) such that for every undirected graph G with n > N vertices and with δ(G) ≥ ckn, every orientation of G contains vertex disjoint copies of TT (h, k) that cover all but at most εn vertices. In the cases k = 2 and k = 3 the result is asymptotically tight. For k ≥ 4, c k cannot be improved to less than 1 - 2-0.5k(1+o(1)).

Original languageEnglish
Pages (from-to)121-133
Number of pages13
Issue number2
StatePublished - 2003


  • Factor
  • Tournament

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Theory and Mathematics


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