A faster FPT algorithm for 3-path vertex cover

Abstract

The k-path vertex cover of a graph G is a subset S of vertices of G such that every path on k vertices in G contains at least one vertex from S. Denote by ψk(G) the minimum cardinality of a k-path vertex cover set in G. The minimum k-path vertex cover problem (k-PVCP) is to find a k-path vertex cover of size ψk(G). In this paper we present an FPT algorithm to the 3-PVCP with runtime O(1.8172snO(1)) on a graph with n vertices. The algorithm constructs a 3-path vertex cover of size at most s in a given graph G, or reports that no such 3-path vertex cover exists in G. This improves previous O(2snO(1)) upper bound by Tu [5] and O(1.882snO(1)) upper bound by Wu [13].