On anti-Kekulé and s-restricted matching preclusion problems

Huazhong Lü (), Xianyue Li () and Heping Zhang ()
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Huazhong Lü: Lanzhou University
Xianyue Li: Lanzhou University
Heping Zhang: Lanzhou University

Journal of Combinatorial Optimization, 2023, vol. 45, issue 4, No 8, 15 pages

Abstract: 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.

Keywords: Anti-Kekulé; Matching preclusion; Conditional matching preclusion; S-restricted matching preclusion; NP-complete; Hypercube (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-023-01034-5

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