Star partitions of graphs

Let G be a graph and n ≥ 2 an integer. We prove that the following are equivalent: (i) there is a partition (V₁,…,V_m) of V (G) such that each V_i induces one of stars K_1,1,…,K_1,n, and (ii) for every subset S of V(G), G\ S has at most n|S| components with the property that each of their blocks is an odd order complete graph. © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 185–190, 1997