Let \(P_4\) denote the path on four vertices. A \(P_4\)-packing of a graph G is a collection of vertex-disjoint copies of \(P_4\) in G. The maximum \(P_4\)-packing problem is to find a \(P_4\)-packing of maximum cardinality in a graph. In this paper, we prove that every simple cubic graph G on v(G) vertices has a \(P_4\)-packing covering at least \(\frac{2v(G)}{3}\) vertices of G and that this lower bound is sharp. Our proof provides a quadratic-time algorithm for finding such a \(P_4\)-packing of a simple cubic graph.

中文翻译：

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立方图的最大 4 顶点路径填充覆盖其至少三分之二的顶点

让\(P_4\)表示四个顶点上的路径。图G的\(P_4\)打包是G中\(P_4\)的顶点不相交副本的集合。最大\(P_4\) -打包问题是在图中找到最大基数的\(P_4\)-打包。在本文中，我们证明v ( G ) 顶点上的每个简单立方图G都有一个\(P_4\)包装，至少覆盖G的\(\frac{2v(G)}{3}\)个顶点，并且这个下界是尖锐的。我们的证明提供了一种二次时间算法来查找简单三次图的\(P_4\)包装。