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Packing and Covering Triangles in Planar Graphs

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Abstract

Tuza conjectured that if a simple graph G does not contain more than k pairwise edge-disjoint triangles, then there exists a set of at most 2k edges that meets all triangles in G. It has been shown that this conjecture is true for planar graphs and the bound is sharp. In this paper, we characterize the set of extremal planar graphs.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, 210016, Nanjing, People’s Republic of China

    Qing Cui

  2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Penny Haxell & Will Ma

Authors
  1. Qing Cui
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  2. Penny Haxell
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  3. Will Ma
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Corresponding author

Correspondence to Qing Cui.

Additional information

Q. Cui was partially supported by Jiangsu Planned Projects for Postdoctoral Research Funds, P. Haxell was partially supported by NSERC and W. Ma was partially supported by an NSERC Undergraduate Student Research Assistantship.

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Cui, Q., Haxell, P. & Ma, W. Packing and Covering Triangles in Planar Graphs. Graphs and Combinatorics 25, 817–824 (2009). https://doi.org/10.1007/s00373-010-0881-5

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  • DOI: https://doi.org/10.1007/s00373-010-0881-5

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