Perfect matchings in planar cubic graphs

A well-known conjecture of Lovász and Plummer from the mid-1970’s, still open, asserts that for every cubic graph G with no cutedge, the number of perfect matchings in G is exponential in |V (G)|. In this paper we prove the conjecture for planar graphs; we prove that if G is a planar cubic graph with no cutedge, then G has at least \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{{{\left| {V(G)} \right|} \mathord{\left/ {\vphantom {{\left| {V(G)} \right|} {655978752}}} \right. \kern-\nulldelimiterspace} {655978752}}}$$\end{document} perfect matchings.