Facial parity edge colouring

Abstract

A facial parity edge colouring of a connected bridgeless plane graph is an edge colouring in which no two face-adjacent edges (consecutive edges of a facial walk of some face) receive the same colour, in addition, for each face α and each colour c, either no edge or an odd number of edges incident with \alpha is coloured with c. From Vizing's theorem it follows that every 3-connected plane graph has a such colouring with at most Δ^* + 1 colours, where Δ^* is the size of the largest face. In this paper we prove that any connected bridgeless plane graph has a facial parity edge colouring with at most 92 colours.