English

Packing and covering directed triangles

Combinatorics 2019-03-11 v2

Abstract

We prove that if a directed multigraph DD has at most tt pairwise arc-disjoint directed triangles, then there exists a set of less than 2t2t arcs in DD which meets all directed triangles in DD, except in the trivial case t=0t=0. This answers affirmatively a question of Tuza from 1990.

Cite

@article{arxiv.1806.08809,
  title  = {Packing and covering directed triangles},
  author = {Jessica McDonald and Gregory J. Puleo and Craig Tennenhouse},
  journal= {arXiv preprint arXiv:1806.08809},
  year   = {2019}
}

Comments

4 pages, 1 figure. The previous version had an error in the argument for the strict inequality in the case where digons are permitted; this version fixes the error

R2 v1 2026-06-23T02:38:53.493Z