Geodesic
On local properties of 1-planar graphs with high minimum degree
Ars Mathematica Contemporanea, Tome 4 (2011) no. 2, pp. 245-254.

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A graph is called 1-planar if there exists its drawing in the plane such that each edge contains at most one crossing. We prove that each 1-planar graph of minimum degree 7 contains a pair of adjacent vertices of degree 7 as well as several small graphs whose vertices have small degrees; we also prove the existence of a 4-cycle with relatively small degree vertices in 1-planar graphs of minimum degree at least 6.
DOI : 10.26493/1855-3974.131.91c
Keywords: 1-planar graph, light graph 
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Dávid Hudák; Tomáš Madaras. On local properties of 1-planar graphs with high minimum degree. Ars Mathematica Contemporanea, Tome 4 (2011) no. 2, pp. 245-254. doi : 10.26493/1855-3974.131.91c. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.131.91c/

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