Abstract
We determine the minimum number of crossings in an outerplanar drawing of the complete bipartite graph K m , n for any values of m and n , which was known only for the specific case when m | n . 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.
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