Proximity thresholds for matching extension in the torus and Klein bottle
A graph G G is said to have the property Ed(m,n) E d ( m , n ) if, given any two disjoint matchings M M and N N such that the edges within M M are pair-wise distance at least d d from each other as are the edges in N N , there is a perfect matching F F in G G such that M?F M ? F and F?N=0? F ? N = 0? . 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.
matching extension torus klein bottle embedding