Facial parity edge colouring of plane pseudographs

Július Czap, Stanislav Jendroľ, František Kardoš, Roman Soták
2012 Discrete Mathematics  
A facial parity edge colouring of a connected bridgeless plane graph is such an edge colouring in which no two face-adjacent edges receive the same colour and, in addition, for each face f and each colour c, either no edge or an odd number of edges incident with f is coloured with c. Let χ ′ p (G) denote the minimum number of colours used in such a colouring of G. In this paper we prove that χ ′ p (G) ≤ 20 for any 2-edge-connected plane graph G. In the case when G is a 3-edge-connected plane
more » ... ph the upper bound for this parameter is 12. For G being 4-edge-connected plane graph we have χ ′ p (G) ≤ 9. On the other hand we prove that some bridgeless plane graphs require at least 10 colours for such a colouring.
doi:10.1016/j.disc.2012.03.036 fatcat:e7fchi7io5he5dxz6glift72ha