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arXiv · 1401.0460

Transitive Triangle Tilings in Oriented Graphs

József Balogh·Allan Lo·Theodore Molla
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Abstract

In this paper, we prove an analogue of Corr\'adi and Hajnal's classical theorem. There exists $n_0$ such that for every $n \in 3\mathbb{Z}$ when $n \ge n_0$ the following holds. If $G$ is an oriented graph on $n$ vertices and every vertex has both indegree and outdegree at least $7n/18$, then $G$ contains a perfect transitive triangle tiling, which is a collection of vertex-disjoint transitive triangles covering every vertex of $G$. This result is best possible, as, for every $n \in 3\mathbb{Z}$, there exists an oriented graph $G$ on $n$ vertices without a perfect transitive triangle tiling in which every vertex has both indegree and outdegree at least $\lceil 7n/18\rceil - 1.$

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József Balogh, Allan Lo, Theodore Molla. 2014-01-02. Transitive Triangle Tilings in Oriented Graphs. https://arxiv.org/abs/1401.0460

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