Parity vertex colouring of plane graphs

A 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 χ p ( G ) . s paper, we prove that χ p ( G ) ≤ 118 for every 2-connected plane graph G .