Abstract:A graph is 2-planar if it has local crossing number two, that is, it can be drawn in the plane such that every edge has at most two crossings. A graph is maximal 2-planar if no edge can be added such that the resulting graph remains 2-planar. A 2-planar graph on n vertices has at most 5n − 10 edges, and some (maximal) 2-planar graphs-referred to as optimal 2-planar -achieve this bound. However, in strong contrast to maximal planar graphs, a maximal 2-planar graph may have fewer than the maximum possible number… Show more
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