Please use this identifier to cite or link to this item:
|Type:||Artigo de periódico|
|Title:||The total-chromatic number of some families of snarks|
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.|
|Editor:||Elsevier Science Bv|
|Appears in Collections:||Artigos e Materiais de Revistas Científicas - Unicamp|
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.