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Some bounds on the generalised total chromatic number of degenerate graphs
The total generalised colourings considered in this paper are colourings of the vertices and
of the edges of graphs satisfying the following conditions:
• each set of vertices of the graph which receive the same colour induces an
m-degenerate graph,
• each set of edges of the graph which receive the same colour induces an n-degenerate
graph, and
• incident elements receive different colours.
Bounds for the least number of colours with which this can be done for all k-degenerate
graphs are obtained.