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Packing and Covering Directed Triangles

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Abstract

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

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Acknowledgements

The first author is supported in part by NSF Grant DMS-1600551.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Auburn University, Auburn, AL, 36849, USA

    Jessica McDonald & Gregory J. Puleo

  2. Department of Mathematical Sciences, University of New England, Biddeford, ME, 04005, USA

    Craig Tennenhouse

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  1. Jessica McDonald
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  2. Gregory J. Puleo
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  3. Craig Tennenhouse
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Correspondence to Jessica McDonald.

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The first author is supported in part by NSF grant DMS-1600551.

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McDonald, J., Puleo, G.J. & Tennenhouse, C. Packing and Covering Directed Triangles. Graphs and Combinatorics 36, 1059–1063 (2020). https://doi.org/10.1007/s00373-020-02167-8

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