Geodesic
Facial parity edge colouring
Ars Mathematica Contemporanea, Tome 4 (2011) no. 2, pp. 255-269.

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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.
DOI : 10.26493/1855-3974.129.be3
Keywords: Plane graph, facial walk, edge colouring. 
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Július Czap; Stanislav Jendroľ; František Kardoš. Facial parity edge colouring. Ars Mathematica Contemporanea, Tome 4 (2011) no. 2, pp. 255-269. doi : 10.26493/1855-3974.129.be3. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.129.be3/

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