Geodesic
On local structure of 1-planar graphs of minimum degree 5 and girth 4
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 385-400

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A graph is 1-planar if it can be embedded in the plane so that each edge is crossed by at most one other edge. We prove that each 1-planar graph of minimum degree 5 and girth 4 contains
Keywords: light graph, 1-planar graph, star, cycle 
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Hudák, Dávid; Madaras, Tomás. On local structure of 1-planar graphs of minimum degree 5 and girth 4. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 385-400. http://geodesic.mathdoc.fr/item/DMGT_2009_29_2_a12/