Connected k-factors in bipartite graphs

Let k,? be two positive integers. An Sk,? is a graph obtained from disjoint K1,k and K1,? by adding an edge between the k-degree vertex in ?-degree K1,?. Sk,?-free containing no induced subgraph isomorphic to Sk,?. In this paper, we show that, for any integers with 2?k??, there exists constant c=c(k,?) such that every connected balanced bipartite minimum degree at least c contains k-factor.