Refined Parameterizations for Computing Colored Cuts in Edge-Colored Graphs

Abstract

In the Colored� problem, the input is a graph� together with an edge-coloring�, two vertices s and t, and a number k. The question is whether there is a set� 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�. First, we consider parameters related to the structure of G. For example, we study parameterization by the number� of edge deletions that are needed to transform G into a graph with maximum degree i. We show that Colored� is-hard when parameterized by�, but fixed-parameter tractable when parameterized by�. Second, we consider parameters related to the coloring�. 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 a rare edge color.