Transitive triangle tilings in oriented graphs

József Balogh, Allan Lo, Theodore Molla

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)64-87
Number of pages24
JournalJournal of Combinatorial Theory. Series B
StatePublished - May 1 2017


  • Minimum semidegree
  • Oriented graphs
  • Packing
  • Transitive triangles

ASJC Scopus subject areas

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


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