Geodesic
On the strong parity chromatic number
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 3, pp. 587-600

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A vertex colouring of a 2-connected plane graph G is a strong parity vertex colouring if for every face f and each colour c, the number of vertices incident with f coloured by c is either zero or odd. Czap et al. in [9] proved that every 2-connected plane graph has a proper strong parity vertex colouring with at most 118 colours. In this paper we improve this upper bound for some classes of plane graphs.
Keywords: plane graph, k-planar graph, vertex colouring, strong parity vertex colouring 
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Czap, Július; Jendroľ, Stanislav; Kardoš, František. On the strong parity chromatic number. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 3, pp. 587-600. http://geodesic.mathdoc.fr/item/DMGT_2011_31_3_a12/