The outerplanar crossing number of the complete bipartite graph

We determine the minimum number of crossings in an outerplanar drawing of the complete bipartite graph K-m,K-n for any values of m and n, which was known only for the specific case when mM. Moreover, we provide a one-to-one correspondence (up to equivalence) between the outerplanar and cylindrical drawings of the complete bipartite graph that preserves the number of crossings but not the crossings themselves. (C) 2022 The Authors. Published by Elsevier B.V.