The existence of a 2-factor in K1, n-free graphs with large connectivity and large edge-connectivity

Ota and Tokuda [2] gave a minimum degree condition for a K1,n-free graph to have a 2factor. Though their condition is best-possible, their sharpness examples have edge-connectivity one. In this paper, we improve their minimum degree condition for K1,n-free graphs with large connectivity or large edge-connectivity. Our bound is sharp, and together with Ota and Tokuda’s theorem, we completely determine those triples (k, n, d) for which every k-edge-connected (kconnected) K1,n-free graph with minimum degree d has a 2-factor.