Cubic bridgeless graphs have more than a linear number of perfect matchings

Lovász and Plummer conjectured in the 1970's that cubic bridgeless graphs have exponentially many perfect matchings. This conjecture has been verified for bipartite graphs by Voorhoeve (1979), and for planar graphs by Chudnovsky and Seymour (2008). In this paper, we provide the first superlinear bound in the general case.