Every n-vertex maximal bipartite IC-plane graph with connectivity at least 2 has at least 3n/2 - 2 edges, and with connectivity at least 3 has at least 2n - 3 edges; both bounds are tight.
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The minimum size of maximal bipartite IC-plane graphs with given connectivity
Every n-vertex maximal bipartite IC-plane graph with connectivity at least 2 has at least 3n/2 - 2 edges, and with connectivity at least 3 has at least 2n - 3 edges; both bounds are tight.