Discussiones Mathematicae Graph Theory 31(3) (2011) 587-600
doi: 10.7151/dmgt.1567

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On the Strong Parity Chromatic Number

J'ulius Czap1, Stanislav Jendrol 2 and Frantisek Kardos 2

1 Department of Applied Mathematics and Business Informatics
Faculty of Economics, Technical University of Košice
Nemcovej 32, SK-04001 Košice, Slovakia
2 Institute of Mathematics, P.J. Safarik University
Jesenn'a 5, SK-04001 Košice, Slovakia


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

2010 Mathematics Subject Classification: 05C15.


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Received 14 September 2009
Revised 23 May 2011
Accepted 24 May 2011