The Maximum 4-Vertex-Path Packing of a Cubic Graph Covers At Least Two-Thirds of Its Vertices

IF 0.6 4区数学 Q3 MATHEMATICS Graphs and Combinatorics Pub Date : 2023-12-20 DOI:10.1007/s00373-023-02732-x

引用次数: 0

Abstract

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.

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立方图的最大 4 顶点路径包装至少覆盖三分之二的顶点

摘要让 $P_4$ 表示四个顶点上的路径。一个图 G 的 $P_4$ -packing是 G 中 $P_4$ 的顶点互不相交的副本的集合。最大 $P_4$ -packing问题是在一个图中找到一个最大心数的$P_4$ -packing。在本文中，我们证明了在 v(G) 个顶点上的每个简单立方图 G 都有一个至少覆盖了 G 的 $\frac{2v(G)}{3}) 个顶点的 \(P_4$ -packing，并且这个下界是尖锐的。我们的证明提供了一种四元时间算法，用于找到简单立方图的$P_4$ -packing。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Graphs and Combinatorics 数学-数学

CiteScore

1.00

自引率

14.30%

发文量

160

审稿时长

6 months

期刊介绍： Graphs and Combinatorics is an international journal devoted to research concerning all aspects of combinatorial mathematics. In addition to original research papers, the journal also features survey articles from authors invited by the editorial board.

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