## Abstract

In this paper, we prove an analogue of Corrádi and Hajnal's classical theorem. There exists n
_{0} such that for every n∈3Z when n≥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∈3Z, 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 ⌈7n/18⌉−1.

Original language | English (US) |
---|---|

Pages (from-to) | 64-87 |

Number of pages | 24 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 124 |

DOIs | |

State | Published - May 1 2017 |

## Keywords

- Minimum semidegree
- Oriented graphs
- Packing
- Transitive triangles

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics