Marthe Bonamy ; Łukasz Bożyk ; Andrzej Grzesik ; Meike Hatzel ; Tomáš Masařík et al. - Tuza's Conjecture for Threshold Graphs

dmtcs:7660 - Discrete Mathematics & Theoretical Computer Science, August 14, 2022, vol. 24, no. 1 - https://doi.org/10.46298/dmtcs.7660
Tuza's Conjecture for Threshold GraphsArticle

Authors: Marthe Bonamy ; Łukasz Bożyk ; Andrzej Grzesik ; Meike Hatzel ; Tomáš Masařík ORCID; Jana Novotná ; Karolina Okrasa ORCID

    Tuza famously conjectured in 1981 that in a graph without k+1 edge-disjoint triangles, it suffices to delete at most 2k edges to obtain a triangle-free graph. The conjecture holds for graphs with small treewidth or small maximum average degree, including planar graphs. However, for dense graphs that are neither cliques nor 4-colorable, only asymptotic results are known. Here, we confirm the conjecture for threshold graphs, i.e. graphs that are both split graphs and cographs, and for co-chain graphs with both sides of the same size divisible by 4.

    https://doi.org/10.46298/dmtcs.7660
    Source: arXiv.org:2105.09871
    Volume: vol. 24, no. 1
    Section: Graph Theory
    Published on: August 14, 2022
    Accepted on: June 3, 2022
    Submitted on: July 9, 2021
    Keywords: Mathematics - Combinatorics,Computer Science - Discrete Mathematics,05C70
    Licence: Attribution 4.0 International (CC BY 4.0)
    Funding:
      Source : OpenAIRE Graph
    • Cuts and decompositions: algorithms and combinatorial properties; Funder: European Commission; Code: 714704
    • Large Discrete Structures; Funder: European Commission; Code: 648509
    • Funder: Natural Sciences and Engineering Research Council of Canada

    Classifications

    Mathematics Subject Classification 20201
    Sources:
    • [1] zbMATH Open.

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