Improved bound on facial parity edge coloring

A facial parity edge coloring of a 2-edge connected plane graph is an edge coloring where no two consecutive edges of a facial trail of any face receive the same color. Additionally, for every face f and every color c either no edge or an odd number of edges incident to f is colored by c. Czap, Jendrol', KardoÅ¡ and Soták (2012)  [6] showed that every 2-edge connected plane graph admits a facial parity edge coloring with at most 20 colors. We improve this bound to 16.