Abstract
In this paper, we consider optimal 1-planar multigraphs, that is, n-vertex multigraph having exactly 4n−8 edges and a drawing on the sphere such that each edge crosses at most one other edge, and that the drawing has no 2-gonal face. We discuss the connectivity of optimal 1-planar multigraphs, and show a generating theorem of such graphs using some operations preserving optimal 1-planarity. Finally, we characterize optimal 1-planar multigraphs if they have no Kt-minor for t≤7.
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