Matching Extension Missing Vertices and Edges in Triangulations of Surfaces

Let G be a 5-connected triangulation of a surface sigma different from the sphere, and let =(sigma) be the Euler characteristic of sigma. Suppose that V0V(G) with |V(G)-V0| even and M and N are two matchings in G-V0 of sizes m and n respectively such that MN=empty set. It is shown that if the pairwise distance between any two elements of V0MN is at least five and the face-width of the embedding of G in sigma is at least max{20m-8-23,6}, then there is a perfect matching M-0 in G-V0 containing M such that M0N=empty set. (C) 2016 Wiley Periodicals, Inc.