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.
@article{129,
title = {Facial parity edge colouring},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {4},
year = {2011},
doi = {10.26493/1855-3974.129.be3},
language = {EN},
url = {http://dml.mathdoc.fr/item/129}
}
Czap, Július; Jendroľ, Stanislav; Kardoš, František. Facial parity edge colouring. ARS MATHEMATICA CONTEMPORANEA, Tome 4 (2011) . doi : 10.26493/1855-3974.129.be3. http://gdmltest.u-ga.fr/item/129/