Faster parameterized algorithms for two vertex deletion problems

Abstract

In the l-Path Vertex Cover problem (resp., the l-Component Order Connectivity problem) the input is an undirected graph G and an integer k. The goal is to decide whether there is a set of vertices of size at most k whose deletion from G results in a graph that does not contain a path with l vertices (resp., does not contain a connected component with at least l vertices). In this paper we give a parameterized algorithm for l-Path Vertex Cover when l=5,6,7, whose running times are O⁎(3.945k), O⁎(4.947k), and O⁎(5.951k), respectively. We also give an algorithm for l-Component Order Connectivity whose running time is O⁎((l−1−ϵl)k) for every l≥4, where ϵl>0 for every l.