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Packing 2- and 3-stars into cubic graphs

Author

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  • Xi, Wenying
  • Lin, Wensong
  • Lin, Yuquan

Abstract

Let i be a positive integer. A complete bipartite graph K1,i is called an i-star, denoted by Si. An {S2,S3}-packing of a graph G is a collection of vertex-disjoint subgraphs of G in which each subgraph is a 2-star or a 3-star. The maximum {S2,S3}-packing problem is to find an {S2,S3}-packing of a given graph containing the maximum number of vertices. The perfect {S2,S3}-packing problem is to answer whether there is an {S2,S3}-packing containing all vertices of the given graph. The perfect {S2,S3}-packing problem is NP-complete in general graphs. In this paper, we prove that the perfect {S2,S3}-packing problem remains NP-complete in cubic graphs and that every simple cubic graph has an {S2,S3}-packing covering at least six-sevenths of its vertices. Our proof infers a quadratic-time algorithm for finding such an {S2,S3}-packing of a simple cubic graph.

Suggested Citation

  • Xi, Wenying & Lin, Wensong & Lin, Yuquan, 2024. "Packing 2- and 3-stars into cubic graphs," Applied Mathematics and Computation, Elsevier, vol. 460(C).
    • Handle: RePEc:eee:apmaco:v:460:y:2024:i:c:s0096300323004563
    DOI: 10.1016/j.amc.2023.128287
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