# On the expected number of perfect matchings in cubic planar graphs

@article{Noy2021OnTE, title={On the expected number of perfect matchings in cubic planar graphs}, author={Marc Noy and Cl'ement Requil'e and Juanjo Ru'e}, journal={ArXiv}, year={2021}, volume={abs/2005.13821} }

A well-known conjecture by Lovasz and Plummer from the 1970s asserted that a bridgeless cubic graph has exponentially many perfect matchings. It was solved in the affirmative by Esperet et al. (Adv. Math. 2011). On the other hand, Chudnovsky and Seymour (Combinatorica 2012) proved the conjecture in the special case of cubic planar graphs. In our work we consider random bridgeless cubic planar graphs with the uniform distribution on graphs with $n$ vertices. Under this model we show that the…

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