Strong parity vertex coloring of plane graphs

Czap and Jendrol’ introduced the notions of strong parity vertex coloring and the corresponding strong parity chromatic number χs. They conjectured that there is a constant bound K on χs for the class of 2-connected plane graphs. We prove that the conjecture is true with K = 97, even with an added restriction to proper colorings. Next, we provide simple examples showing that the sharp bound is at least 8, or at least 10 for proper strong parity vertex colorings.