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

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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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Acknowledgements

We would like to give our thanks to anonymous reviewers for careful reading of this paper and many valuable suggestions.

Funding

This work was supported by NSFC under grant 11771080.

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  1. School of Mathematics, Southeast University, Nanjing, 210096, People’s Republic of China

    Wenying Xi & Wensong Lin

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  1. Wenying Xi
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Correspondence to Wensong Lin.

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Xi, W., Lin, W. The Maximum 4-Vertex-Path Packing of a Cubic Graph Covers At Least Two-Thirds of Its Vertices. Graphs and Combinatorics 40, 5 (2024). https://doi.org/10.1007/s00373-023-02732-x

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  • DOI: https://doi.org/10.1007/s00373-023-02732-x

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