Colored cut games

Morawietz, Nils; Grüttemeier, Niels; Komusiewicz, Christian; Sommer, Frank

doi:10.1016/j.tcs.2022.09.013

Cited by 1 publication

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“…For example, does COLORED (s, t)-CUT admit a kernel for the parameter m >q , the number of edges that are not colored with the q most frequent colors, when q is not constant but bounded by log(|I |)? In this context, we would like to remark that in companion work, we showed that COLORED (s, t)-CUT admits a polynomial kernel when parameterized by the budget parameter k plus the size of a vertex set whose deletion destroys all long paths in G [18]. Are there other combinations of the budget k or color parameterizations with structural graph parameters that yield polynomial kernels?…”

Section: Discussionmentioning

confidence: 96%

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Refined Parameterizations for Computing Colored Cuts in Edge-Colored Graphs

et al. 2022

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In the NP-hard Colored (s,t)-Cut problem, the input is a graph G = (V,E) together with an edge-coloring ℓ : E → C, two vertices s and t, and a number k. The question is whether there is a set $S\subseteq C$ S ⊆ C of at most k colors such that deleting every edge with a color from S destroys all paths between s and t in G. We continue the study of the parameterized complexity of Colored (s,t)-Cut. First, we consider parameters related to the structure of G. For example, we study parameterization by the number ξi of edge deletions that are needed to transform G into a graph with maximum degree i. We show that Colored (s,t)-Cut is W[2]-hard when parameterized by ξ3, but fixed-parameter tractable when parameterized by ξ2. Second, we consider parameters related to the coloring ℓ. We show fixed-parameter tractability for three parameters that are potentially smaller than the total number of colors |C| and provide a linear-size problem kernel for a parameter related to the number of edges with rare edge colors.

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Section: Discussionmentioning

confidence: 96%

“…Moreover, it is open to study color parameterizations for related problems such as LABELED PATH [10] (where we aim to construct an (s, t)-path with a minimum number of colors) and competitive variants of COLORED (s, t)-CUT, where an attacker aims to construct a colored cut and a defender aims to prevent this [18].…”

Section: Discussionmentioning

confidence: 99%