Minimum perfect matchings conjecture for planar 4-connected triangulations

A double wheel is the planar triangulation obtained by joining two vertices to every vertex of a cycle. A planar triangulation is 4-connected if it has no separating set of at most three vertices. Minimum perfect matchings conjecture. For sufficiently large numbers of vertices, double wheels have the minimum number of perfect matchings among all planar 4-connected triangulations. The paper presents this as a conjecture and gives no resolution.