A DEGREE CONDITION FOR THE EXISTENCE OF REGULAR FACTORS IN K-1,K-N-FREE GRAPHS

A graph is called K-1,K-n-free if it contains no K-1,K-n as an induced subgraph. Let n(greater than or equal to 3), r be integers (if r is o dd, r greater than or equal to n - 1). We prove that every K-1,K-n-fre e connected graph G with r\V(G)\ even has an r-factor if its minimum d egree is at least (n + n - 1/r) inverted right perpendicular n/2(n - 1 )r inverted left perpendicular - n-1/r (inverted right perpendicular n /2(n - 1)r inverted right perpendicular)(2) + n - 3. This degree condi tion is sharp. (C) 1996 John Wiley & Sons, Inc.