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.
- Graph algorithms
- Parameterized complexity
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)