Parity vertex colouring of plane graphs

AbstractA proper vertex colouring of a 2-connected plane graph G is a parity vertex colouring if for each face f and each colour c, either no vertex or an odd number of vertices incident with f is coloured with c. The minimum number of colours used in such a colouring of G is denoted by χp(G).In this paper, we prove that χp(G)≤118 for every 2-connected plane graph G