Geodesic
On properties of maximal 1-planar graphs
Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 4, pp. 737-747

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A graph is called 1-planar if there exists a drawing in the plane so that each edge contains at most one crossing. We study maximal 1-planar graphs from the point of view of properties of their diagrams, local structure and hamiltonicity.
Keywords: 1-planar graph, maximal graph 
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Hudák, Dávid; Madaras, Tomáš; Suzuki, Yusuke. On properties of maximal 1-planar graphs. Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 4, pp. 737-747. http://geodesic.mathdoc.fr/item/DMGT_2012_32_4_a9/