Characterizing minimally nn-extendable bipartite graphs

In this paper, it is proved that let GG be a bipartite graph with bipartition (X,Y)(X,Y) and with a perfect matching MM, let GG be an nn-extendable graph, then GG is minimally nn-extendable if and only if, for any two vertices x∈Xx∈X and y∈Yy∈Y such that xy∈E(G)xy∈E(G), there are exactly nn internally disjoint (x,y)M-alternating paths P1,P2,…,PnP1,P2,…,Pn such that Pi(1⩽i⩽n) starts and ends with edges in E(G)⧹ME(G)⧹M.