In the 4-path vertex cover problem, the input is an undirected graph $G$ and an integer $k$. The goal is to decide whether there is a set of vertices $S$ of size at most $k$ such that every path with 4 vertices in $G$ contains at least one vertex of $S$. In this paper we give a parameterized algorithm for 4-path vertex cover whose time complexity is $O^*(2.619^k)$.

中文翻译：

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4-Path Vertex Cover的O∗(2.619k)算法

在4路径顶点覆盖问题中，输入是一个无向图$G$和一个整数$k$。目标是确定是否存在一组最大为 $k$ 的顶点 $S$，使得 $G$ 中具有 4 个顶点的每条路径都包含至少一个 $S$ 的顶点。在本文中，我们给出了时间复杂度为$O^*(2.619^k)$的4路径顶点覆盖的参数化算法。