Vertex-disjoint claws in graphs

Abstract Let δ(G) denote the minimum degree of a graph G . We prove that a graph G of order at least 4 k + 6 with δ ( G ) ⩾ k + 2 contains k pairwise vertex-disjoint K 1,3 ' s . The conditions on the minimum degree and on the order of the graph are best possible in a sense.