Facial parity 9-edge-coloring of outerplane graphs (Q497307)

A connected graph containing no bridge is said to be 2-edge-connected. A facial parity edge coloring of a 2-edge-connected plane graph \(G\) is an edge coloring satisfying the following two conditions: (1) face-adjacent edges of \(G\) receive different colors, and (2) for every color \(c\) and every face f of \(G\), the total number of occurrences of edges colored with \(c\) on a facial trail of \(f\) is odd or zero. It is shown that the minimum number of colors used in coloring any 2-edge-connected outerplane graph \(G\) is less than 10. Furthermore, it is also shown that this bound is tight.