A Survey on the k-Path Vertex Cover Problem

Abstract

Given a graph G = (V, E) and a positive integer k ≥ 2, a k-path vertex cover is a subset of vertices F such that every path on k vertices in G contains at least one vertex from F . A minimum k-path vertex cover in G is a k-path vertex cover with minimum cardinality and its cardinality is called the k-path vertex cover number of G. In the k-path vertex cover problem, it is required to find a minimum k-path vertex cover in a given graph. In this paper, we present a brief survey of the current state of the art in the study of the k-path vertex cover problem and the k-path vertex cover number.

On kernels for d-path vertex cover

“…Hence, another open question is whether such a kernel can be obtained also for say 4-PVC. Further interesting open questions can be found in the recent survey of Tu [29].…”