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Type: Artigo de periódico
Title: The total-chromatic number of some families of snarks
Author: Campos, CN
Dantas, S
de Mello, CP
Abstract: The total-chromatic number chi(T) (C) is the least number of colours needed to colour the vertices and edges of a graph G such that no incident or adjacent elements (vertices or edges) receive the same colour. It is known that the problem of determining the total-chromatic number is NP-hard, and it remains NP-hard even for cubic bipartite graphs. Snarks are simple connected bridgeless cubic graphs that are not 3-edge-colourable. In this paper, we show that the total-chromatic number is 4 for three infinite families of snarks, namely, the Flower Snarks. the Goldberg Snarks, and the Twisted Goldberg Snarks. This result reinforces the conjecture that all snarks have total-chromatic number 4. Moreover, we give recursive procedures to construct a total-colouring that uses 4 colours in each case. (C) 2011 Elsevier B.V. All rights reserved.
Subject: Graph colouring
Country: Holanda
Editor: Elsevier Science Bv
Citation: Discrete Mathematics. Elsevier Science Bv, v. 311, n. 12, n. 984, n. 988, 2011.
Rights: fechado
Identifier DOI: 10.1016/j.disc.2011.02.013
Date Issue: 2011
Appears in Collections:Unicamp - Artigos e Outros Documentos

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