Regular factors in <i>K</i>_1,<i>n</i> free graphs

Abstract

Abstract A graph is said to be K 1, n ‐free, if it contains no K 1, n as an induced subgraph. We prove that for n ⩾ 3 and r ⩾ n −1, if G is a K 1, n ‐free graph with minimum degree at least ( n 2 /4( n −1)) r + (3 n −6)/2 + ( n −1)/4 r , then G has an r ‐factor (in the case where r is even, the condition r ⩾ n −1 can be dropped).