No abstract

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.