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On anti-Kekulé and s-restricted matching preclusion problems

Author

Listed:
  • Huazhong Lü

    (Lanzhou University
    University of Electronic Science and Technology of China)

  • Xianyue Li

    (Lanzhou University)

  • Heping Zhang

    (Lanzhou University)

Abstract

The anti-Kekulé number of a connected graph G is the smallest number of edges whose deletion results in a connected subgraph having no Kekulé structures (perfect matchings). As a common generalization of (conditional) matching preclusion number and anti-Kekulé number of a graph G, we introduce s-restricted matching preclusion number of G as the smallest number of edges whose deletion results in a subgraph without perfect matchings such that each component has at least $$s+1$$ s + 1 vertices. In this paper, we first show that conditional matching preclusion problem and anti-Kekulé problem are NP-complete, respectively, then generalize this result to s-restricted matching preclusion problem. Moreover, we give some sufficient conditions to compute s-restricted matching preclusion numbers of regular graphs. As applications, s-restricted matching preclusion numbers of complete graphs, hypercubes and hyper Petersen networks are determined.

Suggested Citation

  • Huazhong Lü & Xianyue Li & Heping Zhang, 2023. "On anti-Kekulé and s-restricted matching preclusion problems," Journal of Combinatorial Optimization, Springer, vol. 45(4), pages 1-15, May.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:4:d:10.1007_s10878-023-01034-5
    DOI: 10.1007/s10878-023-01034-5
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