id: 05888522
dt: j
an: 05888522
au: Campos, C.N.; Dantas, S.; de Mello, C.P.
ti: The total-chromatic number of some families of snarks.
so: Discrete Math. 311, No. 12, 984-988 (2011).
py: 2011
pu: Elsevier Science B.V. (North-Holland), Amsterdam
la: EN
cc: 
ut: graph colouring; total-colouring; edge-colouring; snark
ci: 
li: doi:10.1016/j.disc.2011.02.013
ab: Summary: The total-chromatic number $χ_T(G)$ 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.
rv: