k-factors in regular graphs

Plesnik in 1972 proved that an ( m − 1)-edge connected m -regular graph of even order has a 1-factor containing any given edge and has another 1-factor excluding any given m − 1 edges. Alder et al. in 1999 showed that if G is a regular (2 n + 1)-edge-connected bipartite graph, then G has a 1-factor containing any given edge and excluding any given matching of size n . In this paper we obtain some sufficient conditions related to the edge-connectivity for an n -regular graph to have a k -factor containing a set of edges and (or) excluding a set of edges, where 1 ≤ k ≤ n /2. In particular, we generalize Plesnik’s result and the results obtained by Liu et al . in 1998, and improve Katerinis’ result obtained 1993. Furthermore, we show that the results in this paper are the best possible.