Transitive tournament tilings in oriented graphs with large minimum total degree

2019/06/18 by DeBiasio, Louis, Lo, Allan, Molla, Theodore +1
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.07648

Abstract

Let 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 T₄'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 T_k's.

Related

• Tiling transitive tournaments and their blow-ups
• Tiling directed graphs with tournaments
• An extension of the Hajnal-Szemeredi theorem to directed graphs
• Subdivisions of digraphs in tournaments
• Partitioning transitive tournaments into isomorphic digraphs