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An upper bound for the total chromatic number

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Abstract

The total chromatic number,χ″(G), of a graphG, is defined to be the minimum number of colours needed to colour the vertices and edges of a graph in such a way that no adjacent vertices, no adjacent edges and no incident vertex and edge are given the same colour. This paper shows that\(\chi ''\left( G \right) \leqslant \chi '\left( G \right) + 2\sqrt { \chi \left( G \right)} \), whereχ(G) is the vertex chromatic number andχ′(G) is the edge chromatic number of the graph.

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Cambridge, 16 Mill Lane, Cambridge, England

    H. R. Hind

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  1. H. R. Hind
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Partially supported by ORS grant ORS/84120

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Hind, H.R. An upper bound for the total chromatic number. Graphs and Combinatorics 6, 153–159 (1990). https://doi.org/10.1007/BF01787726

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  • DOI: https://doi.org/10.1007/BF01787726

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