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

We focus on a specific class of planar cubic bridgeless graphs, namely the klee-graphs. K4 is the smallest klee-graph and having a klee-graph G we create another klee-graph by replacing any vertex of G by a triangle, i.e., applying Y∆ operation. In this paper, we prove that every klee-graph with n ≥ 8 vertices has at least 3 · 2 perfect matchings, improving the 2 bound inherited from the general result for planar cubic bridgeless graphs by Chudnovsky and Seymour from 2008.