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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 solveddoi:10.1137/140975279 fatcat:5w6bkeixprhctnjopisjxg3c3e