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Lovasz and Plummer conjectured in the 1970's that cubic bridgeless graphshave exponentially many perfect matchings. This conjecture has been verifiedfor bipartite graphs by Voorhoeve in 1979, and for planar graphs by Chudnovskyand Seymour in 2008, but in general only linear bounds are known. In thispaper, we provide the first superlinear bound in the general case.

A superlinear bound on the number of perfect matchings in cubic bridgeless graphs