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arXiv · 2201.03397

A Survey on the k-Path Vertex Cover Problem

Jianhua Tu
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Abstract

Given a graph $G=(V,E)$ and a positive integer $k\ge2$, 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 {\it $k$-path vertex cover number} of $G$. In the {\it $k$-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.

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Jianhua Tu. 2022-01-10. A Survey on the k-Path Vertex Cover Problem. https://arxiv.org/abs/2201.03397

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