Facial parity edge colouring of plane pseudographs
Résumé
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 graph 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.
Domaines
Mathématique discrète [cs.DM]
Origine : Fichiers produits par l'(les) auteur(s)
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