  The Hadwiger number of a graph G is the largest integer h such that G has the
complete graph K_h as a minor. We show that the problem of determining the
Hadwiger number of a graph is NP-hard on co-bipartite graphs, but can be solved
in polynomial time on cographs and on bipartite permutation graphs. We also
consider a natural generalization of this problem that asks for the largest
integer h such that G has a minor with h vertices and diameter at most $s$. We
show that this problem can be solved in polynomial time on AT-free graphs when
s>=2, but is NP-hard on chordal graphs for every fixed s>=2.
