Parameterized Algorithms for Module Map Problems

Abstract

We introduce and study the NP-hard Module Map problem which has as input a graph G with red and blue edges and asks to transform G by at most k edge modifications into a graph which does not contain a two-colored \(K_3\), that is, a triangle with two blue edges and one red edge, a blue \(P_3\), that is, a path on three vertices with two blue edges, and a two-colored \(P_3\), that is, a path on three vertices with one blue and one red edge, as induced subgraph. We show that Module Map can be solved in \(\mathcal {O}(2^k \cdot n^3)\) time on n-vertex graphs and present a problem kernelization with \(\mathcal {O}(k^2)\) vertices.