15 research outputs found
Transitive Triangle Tilings in Oriented Graphs
In this paper, we prove an analogue of Corr\'adi and Hajnal's classical
theorem. There exists such that for every when the following holds. If is an oriented graph on vertices and every
vertex has both indegree and outdegree at least , then contains a
perfect transitive triangle tiling, which is a collection of vertex-disjoint
transitive triangles covering every vertex of . This result is best
possible, as, for every , there exists an oriented graph
on vertices without a perfect transitive triangle tiling in which every
vertex has both indegree and outdegree at least Comment: To appear in Journal of Combinatorial Theory, Series B (JCTB
Transitive tournament tilings in oriented graphs with large minimum total degree
Let be the transitive tournament on vertices. We show that
every oriented graph on vertices with minimum total degree
can be partitioned into vertex disjoint '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
's.Comment: 18 pages, 3 figures. Minor updates based on referee report