Let G = (V,A,E) be a mixed graph and co : V → {1, 2,...,λ} a function such that co is a proper colouring of the underlying graph, Und(G), and co(u) ≠ co(y) when co(v) = co(x), for every pair of arcs (u,v) and (x,y). Such a function is called a proper oriented λ − colouring of G. The number of proper oriented λ–colourings of G, denoted fo(G,λ), is a polynomial in λ. We call fo(G,λ) the mixed-chromatic polynomial of G. In this thesis we will first present the basic theory of the mixed-chromatic poly-nomial. This theory will include computational tools and results concerning the coefficients of fo(G,λ). Next, we will consider the question of chromatic uniqueness and invariance of mixed graphs. Lastly, we reformulate a contract-delete recurrence for chromatic polynomials in order to enumerate various colourings, such as k−frugal λ−colourings. / Graduate
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/11070 |
| Date | 27 August 2019 |
| Creators | Wheeler, Mackenzie J. |
| Contributors | MacGillivray, Gary |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
| Rights | Available to the World Wide Web |
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