f-Factors in bipartite (mf)-graphs

AbstractKaterinis and Tsikopoulos (Graphs. Combin. 12 (1996) 327) give sufficient conditions for a regular bipartite graph to have a perfect matching excluding a set of edges. In this paper, we give a necessary and sufficient condition for a bipartite graph to have an f-factor containing a set of edges and excluding another set of edges and discuss some applications of this condition. In particular, we obtain some sufficient conditions related to connectivity and edge-connectivity for a bipartite (mf)-graph to have an f-factor with special properties and generalize the results in (Graphs. Combin. 12 (1996) 327). The results in this paper are in some sense best possible