Directed 3-cycle decompositions of complete directed graphs with quadratic leaves

Liqun Pu*, Hung-Lin Fu, Hao Shen

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

Let G be a vertex-disjoint union of directed cycles in the complete directed graph Dt, let | E (G) | be the number of directed edges of G and suppose G ≠ over(C, ⇀)2 ∪ over(C, ⇀)3 or over(C, ⇀)5 if t = 5, and G ≠ over(C, ⇀)3 ∪ over(C, ⇀)3 if t = 6. It is proved in this paper that for each positive integer t, there exist over(C, ⇀)3-decompositions for Dt - G if and only if t (t - 1) - | E (G) | ≡ 0 (mod 3).

Original languageEnglish
Pages (from-to)4705-4715
Number of pages11
JournalDiscrete Mathematics
Volume309
Issue number14
DOIs
StatePublished - 28 Jul 2009

Keywords

  • Complete directed graph
  • Mendelsohn triples
  • Packing

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