Abstract
A graph G is said to have the property Ed(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⊆F and F∩N=0̸. 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.
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