Tuza's Conjecture for Threshold Graphs
Combinatorics
2023-06-22 v3 Discrete Mathematics
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.
Keywords
Cite
@article{arxiv.2105.09871,
title = {Tuza's Conjecture for Threshold Graphs},
author = {Marthe Bonamy and Łukasz Bożyk and Andrzej Grzesik and Meike Hatzel and Tomáš Masařík and Jana Novotná and Karolina Okrasa},
journal= {arXiv preprint arXiv:2105.09871},
year = {2023}
}
Comments
14 pages, 11 figures, Accepted to European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB) 2021