On the Strong Parity Chromatic Number

International audienceA 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. [Discrete Math. 311 (2011) 512-520] 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