Abstract
This chapter treats a subject occurring quite often in Graph Theory, namely colourings. First, we show the relationship between colourings and partial orderings (as studied in Section 7.5) and mention ‘perfect’ graphs. Then we prove the two main theorems about colourings of vertices and edges (namely the Theorems of Brooks and Vizing). Finally, we consider edge colourings of Cayley graphs; these are graphs which are defined using groups. We will barely scractch the surface of a vast area in this chapter; for a detailed study of colouring problems we refer the reader to the monograph by Jensen and Toft (1995).
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© 1999 Springer-Verlag Berlin Heidelberg
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Jungnickel, D. (1999). Colourings. In: Graphs, Networks and Algorithms. Algorithms and Computation in Mathematics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03822-2_8
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DOI: https://doi.org/10.1007/978-3-662-03822-2_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-03824-6
Online ISBN: 978-3-662-03822-2
eBook Packages: Springer Book Archive