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arXiv · 2105.09871

Tuza's Conjecture for Threshold Graphs

Marthe Bonamy·Łukasz Bożyk·Andrzej Grzesik·Meike Hatzel·Tomáš Masařík·Jana Novotná·Karolina Okrasa
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Abstract

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.

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Marthe Bonamy, Łukasz Bożyk, Andrzej Grzesik, Meike Hatzel, Tomáš Masařík, Jana Novotná, Karolina Okrasa. 2021-05-20. Tuza's Conjecture for Threshold Graphs. https://doi.org/10.46298/dmtcs.7660

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