Rotation numers for complete bipartite graphs

A rooted graph is a pair (G, x) where G is a simple undirected graph and x ? V(G). If G if rooted at x, then its rotation number h(G, x) is teh minimum number of edges in a graph F, of the same order as G, such that for all v ? V(F) we can find a copy of G in F with the root x at v. Rotation numbers for complete bipartite graphs were itroduced in [4] by Cockayne and Lorimer. Several cases were evaluated by Bollobás and Cockayne in [2], and in this paper we give a full solution.