Transitive tournament tilings in oriented graphs with large minimum total degree

Abstract

Let ${\vec{T}}_k$ be the transitive tournament on $k$ vertices. We show that every oriented graph on $n=4m$ vertices with minimum total degree $(11/12+o(1))n$ can be partitioned into vertex disjoint ${\vec{T}}_4$'s, and this bound is asymptotically tight. We also improve the best known bound on the minimum total degree for partitioning oriented graphs into vertex disjoint ${\vec{T}}_k$'s.

18 pages, 3 figures. Minor updates based on referee reports