On the restricted matching extension of graphs in surfaces

Abstract: A connected graph with at least vertices is said to have property if for any two disjoint matchings and of sizes and respectively, has a perfect matching such that and . Let be the smallest integer such that no graphs embedded in the surface are -extendable. It has been shown that no graphs embedded in some scattered surfaces as the sphere, projective plane, torus and Klein bottle are . In this paper, we show that this result holds for all surfaces. Furthermore, we obtain that for each integer , if a graph embedded in a surface has too many vertices, then does not have property . [Copyright &y& Elsevier]