Let $H$ be a fixed undirected graph on $k$ vertices. The $H$-hitting set problem asks for deleting a minimum number of vertices from a given graph $G$ in such a way that the resulting graph has no copies of $H$ as a subgraph. This problem is a special case of the hypergraph vertex cover problem on $k$-uniform hypergraphs, and thus admits an efficient $k$-factor approximation algorithm. The purpose of this article is to investigate the question that for which graphs $H$ this trivial approximation factor $k$ can be improved.

中文翻译：

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命中子图的近似算法

假设$ H $是$ k $顶点上的固定无向图。$ H $命中集问题要求以给定图$ G $删除最小数量的顶点的方式，使所得图没有$ H $副本作为子图。此问题是$ k $一致超图上的超图顶点覆盖问题的特例，因此可以采用有效的$ k $因子近似算法。本文的目的是研究以下问题：对于平凡的逼近因子$ k $，可以为哪些图形$ H $进行改进。