Enumerating Minimal Subset Feedback Vertex Sets

Abstract

The Subset Feedback Vertex Set problem takes as input a pair (G,S), where G=(V,E) is a graph with weights on its vertices, and S⊆V. The task is to find a set of vertices of total minimum weight to be removed from G, such that in the remaining graph no cycle contains a vertex of S. We show that this problem can be solved in time O(1.8638 n ), where n=|V|. This is a consequence of the main result of this paper, namely that all minimal subset feedback vertex sets of a graph can be enumerated in time O(1.8638 n ).