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Disjoint path covers of star graphs

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  • Qiao, Hongwei
  • Meng, Jixiang

Abstract

Given a graph G, let S and T be two vertex-disjoint subsets of equal size k of G. A k-disjoint path cover of G corresponding to S and T is the union of k vertex-disjoint paths among S and T that spans G. If every vertex of S should be joined to a prescribed vertex in T, it is defined to be paired, otherwise it is unpaired. Let STn be a star graph with bipartition V0 and V1. Let S⊆V0 and T⊆V1 be two vertex subsets of equal size k. It is shown in this paper that STn admits an unpaired k-disjoint path cover between S and T, where k≤n−2 and n≥4. In view of the degree of STn, this result is optimal.

Suggested Citation

  • Qiao, Hongwei & Meng, Jixiang, 2025. "Disjoint path covers of star graphs," Applied Mathematics and Computation, Elsevier, vol. 487(C).
    • Handle: RePEc:eee:apmaco:v:487:y:2025:i:c:s0096300324005599
    DOI: 10.1016/j.amc.2024.129098
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    References listed on IDEAS

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    1. Yang, Yayu & Zhang, Mingzu & Meng, Jixiang, 2024. "Link fault tolerance of BC networks and folded hypercubes on h-extra r-component edge-connectivity," Applied Mathematics and Computation, Elsevier, vol. 462(C).
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