Authors: Tomas Kaiser ¹; Ondrej Rucky ¹; Matej Stehlik ²; Riste Škrekovski ³

• 1 department of mathematics and institute of computer science
• 2 Optimisation Combinatoire
• 3 Faculty of Mathematics and Physics [Ljubljana]

A strong parity vertex coloring of a 2-connected plane graph is a coloring of the vertices such that every face is incident with zero or an odd number of vertices of each color. We prove that every 2-connected loopless plane graph has a strong parity vertex coloring with 97 colors. Moreover the coloring we construct is proper. This proves a conjecture of Czap and Jendrol' [Discuss. Math. Graph Theory 29 (2009), pp. 521-543.]. We also provide examples showing that eight colors may be necessary (ten when restricted to proper colorings).