Abstract
A graph G is said to have the property E-d (m, n) if, given any two disjoint matchings M and N such that the edges within M are pair-wise distance at least d from each other as are the edges in N, there is a perfect matching F in G such that M subset of F and F boolean AND N = phi. This property has been previously studied for planar triangulations as well as projective planar triangulations. Here this study is extended to triangulations of the torus and Klein bottle. (C) 2011 Elsevier B.V. All rights reserved.