Minimum k-path vertex cover
Combinatorics
2011-08-02 v2 Computational Complexity
Discrete Mathematics
Abstract
A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. Denote by \psi_k(G) the minimum cardinality of a k-path vertex cover in G. It is shown that the problem of determining \psi_k(G) is NP-hard for each k \geq 2, while for trees the problem can be solved in linear time. We investigate upper bounds on the value of \psi_k(G) and provide several estimations and exact values of \psi_k(G). We also prove that \psi_3(G) \leq (2n + m)/6, for every graph G with n vertices and m edges.
Keywords
Cite
@article{arxiv.1012.2088,
title = {Minimum k-path vertex cover},
author = {Boštjan Brešar and František Kardoš and Ján Katrenič and Gabriel Semanišin},
journal= {arXiv preprint arXiv:1012.2088},
year = {2011}
}
Comments
submitted manuscript