Broere, IzakSemanišin, Gabriel2017-03-292017-06Broere, I & Semanišin, G 2017, 'Some bounds on the generalised total chromatic number of degenerate graphs',Information Processing Letters, vol. 122, pp. 30-33.0020-0190 (print)1872-6119 (online)10.1016/j.ipl.2017.02.008http://hdl.handle.net/2263/59566The 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.en© 2017 Elsevier B.V. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Information Processing Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. A definitive version was subsequently published in Information Processing Letter, vol. 122, pp. 30-33, 2017. doi : 10.1016/j.ipl.2017.02.008.Combinatorial problemsTotal colouring numberGraph propertyk-Degenerate graphPostprint Article