Geodesic
Unavoidable set of face types for planar maps
Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 2, pp. 123-141

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The type of a face f of a planar map is a sequence of degrees of vertices of f as they are encountered when traversing the boundary of f. A set of face types is found such that in any normal planar map there is a face with type from . The set has four infinite series of types as, in a certain sense, the minimum possible number. An analogous result is applied to obtain new upper bounds for the cyclic chromatic number of 3-connected planar maps.
Keywords: normal planar map, plane graph, type of a face, unavoidable set, cyclic chromatic number 
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     title = {Unavoidable set of face types for planar maps},
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Horňák, Mirko; Jendrol, Stanislav. Unavoidable set of face types for planar maps. Discussiones Mathematicae. Graph Theory, Tome 16 (1996) no. 2, pp. 123-141. http://geodesic.mathdoc.fr/item/DMGT_1996_16_2_a3/