Characterizing minimally n-extendable bipartite graphs

In this paper, it is proved that let G be a bipartite graph with bipartition (X, Y) and with a perfect matching M, let G be an n-extendable graph, then G is minimally n-extendable if and only if, for any two vertices x epsilon X and y epsilon Y such that xy epsilon E(G), there are exactly n internally disjoint (x, y) M-alternating paths P-1, P-2,..., P-n such that P-i (1 <= i <= n) starts and ends with edges in E(G)\M. (C) 2007 Elsevier B.V. All rights reserved.