Edge Proximity Conditions for Extendability in Planar Triangulations

A graph G with at least 2m+2 vertices is said to be distance d m-extendable if for any matching M of G with m edges in which the edges lie at distance at least d pairwise, there exists a perfect matching of G containing M. In this article we prove that every 5-connected triangulation on the plane of even order is distance 3 9-extendable and distance 4 m-extendable for any m.