  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^*(1.588^k) for deciding k-CO-PATH SET, significantly improving the previously
best known O^*(2.17^k) of Feng, Zhou, and Wang (2015). Our main tool is a new
O^*(4^{tw(G)}) algorithm for CO-PATH SET using the Cut&Count framework, where
tw(G) denotes treewidth. In general graphs, we combine this with a branching
algorithm which refines a 6k-kernel into reduced instances, which we prove have
bounded treewidth.
