Characterizing defect nn-extendable bipartite graphs with different connectivities

A near perfect matching is a matching saturating all but one vertex in a graph. If GG is a connected graph and any nn independent edges in GG are contained in a near perfect matching where nn is a positive integer and n⩽(|V(G)|-2)/2n⩽(|V(G)|-2)/2, then GG is said to be defect nn-extendable. This paper first shows that the connectivity of defect nn-extendable bipartite graphs can be any integer. Then it characterizes defect nn-extendable bipartite graph GG with κ(G)=1κ(G)=1, κ(G)⩾2κ(G)⩾2 and κ(G)⩾nκ(G)⩾n, respectively. Some properties for defect nn-extendable bipartite graphs with different connectivities are also given.