Geodesic
On doubly light vertices in plane graphs
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 2, pp. 333-344.

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A vertex is said to be doubly light in a family of plane graphs if its degree and sizes of neighbouring faces are bounded above by a finite constant. We provide several results on the existence of doubly light vertices in various families of plane graph.
Keywords: plane graph, doubly light vertex 
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Kozáková, Veronika; Madaras, Tomáš. On doubly light vertices in plane graphs. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 2, pp. 333-344. http://geodesic.mathdoc.fr/item/DMGT_2011_31_2_a9/

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