A degree condition for the existence of regular factors in K1, n-free graphs

A graph is called K_{1, n}-free if it contains no K_{1, n} as an induced subgraph. Let n(≥3), r be integers (if r is odd, r ≥ n − 1). We prove that every K_{1, n}-free connected graph G with r|V(G)| even has an r-factor if its minimum degree is at least. $ left(n+{{n-1}over{r}}right) leftlceil {nover{2(n-1)}}r rightrceil - {{n-1}over{r}}left(leftlceil {nover{2(n-1)}}r rightrceil right)^2+n-3. $ This degree condition is sharp. © 1996 John Wiley & Sons, Inc.