Two conditions for a bipartite graph to be a k－deleted graph

A κ-regular spanning subgraph of graph G is called a κ-factor of G. Graph G is called a κ-deleted graph if G -e has a κ-factor for each edge e. A graph G = (X, Y) with bipartition (X, Y) is called a bipartite graph if every edge of G has one endpoint in X and the other in Y.It is proved that a bipartite graph G = (X, Y) with |X| = |Y| is a κ-deleted graph if and only if κ | S |≤ rl + 2r2 +…+ κ( rκ +…+ r△ ) -e(S) for all S lontain in X. Using this result we give a sufficient neighborhood condition for a bipartite to be a κ-deleted graph.