Abstract
In the previous chapter, we proved that for any constant ∈ > 0, graphs in which every vertex is ∈Δ-sparse have a Δ + C(∈) total colouring. In this chapter, we will show how to modify that proof to handle graphs that include dense vertices, thereby proving Theorem 17.1. To do so, we make use of the decomposition from Chap. 15.
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© 2002 Springer-Verlag Berlin Heidelberg
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Molloy, M., Reed, B. (2002). Near Optimal Total Colouring II: General Graphs. In: Graph Colouring and the Probabilistic Method. Algorithms and Combinatorics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04016-0_18
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DOI: https://doi.org/10.1007/978-3-642-04016-0_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04015-3
Online ISBN: 978-3-642-04016-0
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