Facial Parity 9-Edge-Coloring of Outerplane Graphs.

A facial parity edge-coloring of a $$2$$ -edge-connected plane graph is such an edge-coloring in which no two face-adjacent edges receive the same color and in addition, for each face $$f$$ and each color $$c$$ either no edge or an odd number of edges incident with $$f$$ is colored with $$c$$ . Let $$\chi _p^\prime (G)$$ denote the minimum number of colors used in such a coloring of $$G$$ . In this paper we prove that $$\chi _p^\prime (G)\le 9$$ for any $$2$$ -edge-connected outerplane graph $$G$$ with one exception. Moreover, we show that this bound is tight. [ABSTRACT FROM AUTHOR]