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The total chromatic number of regular graphs whose complement is bipartite

✍ Scribed by J.K. Dugdale; A.J.W. Hilton

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 705 KB
Volume: 126
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90255-0

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✦ Synopsis

We show that a regular graph G of order at least 6 whose complement c is bipartite has total chromatic number d(G) + 1 if and only if (i) G is not a complete graph, and (ii) G#K when n is even.

As an aid in"';he proof of this, we also show that , for n>4, if the edges of a Hamiltonian path of Kzn are coloured with 2n-1 colours, each edge receiving a different colour, then this can be extended to an edge-colouring of K," with the same set of 2n-1 colours.

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