Abstract

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

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