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 ψ k (G) the minimum cardinality of a k-path vertex cover in G. It is shown that the problem of determining ψ k (G) is NP-hard for each k ≥ 2, while for trees the problem can be solved in linear time. We investigate upper bounds on the value of ψ k (G) and provide several estimations and exact values of ψ k (G). We also prove that ψ 3 (G) ≤ (2n + m)/6, for every graph G with n vertices and m edges.
Unfortunately, computing a minimum k-path cover is NP-hard REF .
Minimum k-path vertex cover
Discret. Appl. Math.
Discret. Appl. Math.
Computer Science Mathematics