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math.CO2021★ 2 cited
Tuza's Conjecture for Threshold Graphs
Marthe Bonamy, Łukasz Bożyk, Andrzej Grzesik +4
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…
math.CO2021
On objects dual to tree-cut decompositions
Łukasz Bożyk, Oscar Defrain, Karolina Okrasa +1
Tree-cut width is a graph parameter introduced by Wollan that is an analogue of treewidth for the immersion order on graphs in the following sense: the tree-cut width of a graph is…
math.CO2021
On the Erdős-Pósa property for immersions and topological minors in tournaments
Łukasz Bożyk, Michał Pilipczuk
We consider the Erdős-Pósa property for immersions and topological minors in tournaments. We prove that for every simple digraph , , and tournament , the fol…