Kernelization of the 3-path vertex cover problem

The 3-path vertex cover problem is an extension of the well-known vertex cover problem. It asks for a vertex set S subset of V(G) of minimum cardinality such that G - S only contains independent vertices and edges. In this paper we will present a polynomial algorithm which computes two disjoint sets T-1, T-2 of vertices of G such that (i) for any 3-path vertex cover S' in G[T-2], S' U T-1 is a 3-path vertex cover in G, (ii) there exists a minimum 3-path vertex cover in G which contains T-1 and (iii) vertical bar T-2 vertical bar <= 6 . psi(3)(G[T-2]), where psi(3)(G) is the cardinality of a minimum 3-path vertex cover and T-2 is the kernel of G. (C) 2015 Elsevier B.V. All rights reserved.