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A bound on the number of perfect matchings in Klee-graphs

Abstract : The famous conjecture of Lovász and Plummer, very recently proven by Esperet et al. (2011), asserts that every cubic bridgeless graph has exponentially many perfect matchings. In this paper we improve the bound of Esperet et al. for a specific subclass of cubic bridgeless graphs called the Klee-graphs. We show that every Klee-graph with n ≥8 vertices has at least 3 *2(n+12)/60 perfect matchings.
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Marek Cygan, Marcin Pilipczuk, Riste Škrekovski. A bound on the number of perfect matchings in Klee-graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2013, Vol. 15 no. 1 (1), pp.37--52. ⟨hal-00990605⟩

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