The Maximum Vertex Coverage problem (abbreviated as MVC) is to maximum the number of edges covered by a set of vertices of size exactly K on a graph. This problem is the dual of the vertex cover problem and has attracted a lot of interests in the literature of approximation algorithm. So far, the best approximation factor for the MVC problem is 3/4, which is obtained using an LP-rounding method. The main results of this paper are new approximation algorithms for MVC on cubic graphs and 3-bounded graphs (the vertex degrees are at most 3). The approximation factor on cubic graphs is 79/90 (≈0.878), which is tight by analyzing the existence of a feasible solution for a linear programming system. This algorithm can also be extended to 3-bounded graphs and guarantees an approximation factor of 19/24 (≈0.792).

最大顶点覆盖问题（缩写为 MVC）是最大化图上一组大小正好为K的顶点所覆盖的边数。这个问题是顶点覆盖问题的对偶问题，在逼近算法的文献中引起了很多兴趣。到目前为止，MVC 问题的最佳近似因子是 3/4，这是使用 LP 舍入方法获得的。本文的主要成果是MVC在三次图和3有界图（顶点度最多为3）上的新近似算法。三次图上的逼近因子为 79/90 (≈0.878)，通过分析线性规划系统的可行解的存在性，这是严格的。该算法还可以扩展到 3 界图并保证近似因子为 19/24 (≈0.792)。