Matching extension in quadrangulations of the torus
Robert E. L. Aldred, Qiuli Li, Michael D. Plummer, Heping Zhang · Australas. J Comb. · 2013
A graph G is said to have the property E(m,n) if, given any two disjoint matchings M and N where |M | = m and |N | = n respectively and M ∩ N = ∅, there is a perfect matching F in G such that M ⊆ F and F ∩N = ∅. This property has been previously studied for triangulations of the plane, projective plane, torus and Klein bottle. Here this study is extended to quadrangulations of the torus.