Minimum k-path vertex cover

Details Minimum k-path vertex cover Minimum k-path vertex cover

2010-12-09

arxiv.org/abs/1012.2088v2

Discrete Applied Mathematics Volume 159, Issue 12, 28 July 2011, Pages 1189-1195

Mathematics

Combinatorics

submitted manuscript

Scientific paper

10.1016/j.dam.2011.04.008

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.

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