A Fast Parameterized Algorithm for Co-Path Set

The k-Co-Path Set problem asks, given a graph G and a positive integer k, whether one can delete k edges from G so that the remainder is a collection of disjoint paths. We give a linear-time fpt algorithm with complexity O∗(1.588k) for deciding k-Co-Path Set, significantly improving the previously best known O∗(2.17k) of Feng, Zhou, and Wang (2015). We also describe a new O∗(4tw(G)) algorithm for Co-Path Set using the Cut&Count framework. In general graphs, we combine this with a branching algorithm which refines a 6k-kernel into reduced instances, which we prove have bounded treewidth.