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Packing and Covering Triangles in Bilaterally-Complete Tripartite Graphs

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A Correction to this article was published on 30 December 2024

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Abstract

We use Menger’s Theorem and König’s Line Colouring Theorem to show that in any tripartite graph with two complete (bipartite) sides the maximum number of pairwise edge-disjoint triangles equals the minimum number of edges that meet all triangles. This generalizes the corresponding result for complete tripartite graphs given by Lakshmanan, et al.

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Acknowledgements

We would like to thank You Rao for her translation of Mao Cheng’s paper into English, and Donovan Hare for helpful comments on this manuscript.

Funding

The first author was supported by Mitacs through a Mitacs Globalink Research Internship while visiting UBC Okanagan. The second author was supported by an Undergraduate Research Award from the I.K. Barber Faculty of Science at UBC Okanagan.

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Authors and Affiliations

  1. Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Naivedya Amarnani

  2. Mathematics, University of British Columbia–Okanagan, Kelowna, British Columbia, Canada

    A De Burgos & Wayne Broughton

  3. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, Netherlands

    Naivedya Amarnani

Authors
  1. Naivedya Amarnani
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  2. A De Burgos
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  3. Wayne Broughton
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Correspondence to Wayne Broughton.

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The first author was supported by Mitacs through a Mitacs Globalink Research Internship while visiting UBC Okanagan. The second author was supported by an Undergraduate Research Award from the I.K. Barber Faculty of Science at UBC Okanagan.

The original article hs been corrected to update affiliation for first author Naivedya Amarnani as Delft Institute of Applied Mathematics, Delft University of Technology, Delft, Netherlands and the second author’s last name is “De Burgos”; he should be listed in the citation as “De Burgos, A.

The first author was supported by Mitacs through a Mitacs Globalink Research Internship while visiting UBC Okanagan. The second author was supported by an Undergraduate Research Award from the I.K. Barber Faculty of Science at UBC Okanagan.

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Amarnani, N., De Burgos, A. & Broughton, W. Packing and Covering Triangles in Bilaterally-Complete Tripartite Graphs. Graphs and Combinatorics 40, 112 (2024). https://doi.org/10.1007/s00373-024-02845-x

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  • DOI: https://doi.org/10.1007/s00373-024-02845-x

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