Connected [a, b]-factors in K1,n-free graphs containing an [a, b]-factor

A graph G is called K-1,K-n-free if G has no induced subgraph isomorphic to K-1,K-n. Let n, a, and b be integers with n greater than or equal to 3, a greater than or equal to 1, and b greater than or equal to a(n - 2) + 2. We prove that every connected K-1,K-n-free graph G has a connected [a,b]-factor if G contains an [a,b]-factor. This result is sharp in the sense that there exists a connected K-l,K-n-free graph which has an [a,b]-factor but no connected [a,b]-factor for b less than or equal to a(n - 2) + 1. (C) 1999 Elsevier Science B.V. All rights reserved.