Geodesic
On the structure of plane graphs of minimum face size 5
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 3, pp. 403-411

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A subgraph of a plane graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. It is known that a plane graph of minimum face size 5 contains light paths and a light pentagon. In this paper we show that every plane graph of minimum face size 5 contains also a light star K_1,3 and we present a structural result concerning the existence of a pair of adjacent faces with degree-bounded vertices.
Keywords: plane graph, light graph, face size 
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Madaras, Tomás. On the structure of plane graphs of minimum face size 5. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 3, pp. 403-411. http://geodesic.mathdoc.fr/item/DMGT_2004_24_3_a3/