A 2-dipath k-colouring of an oriented graph G is an assignment of k colours, 1,2, . . . , k,
to the vertices of G such that vertices joined by a directed path of length two are assigned different colours. The 2-dipath chromatic number is the minimum number
of colours needed in such a colouring. There are two possible models, depending on whether adjacent vertices must also be assigned different colours.
For both models of 2-dipath colouring we develop the basic theory, including characterizing
the oriented graphs that can be 2-dipath coloured using a small number of colours, finding bounds on the 2-dipath chromatic number, determining the complexity of deciding the existence of a 2-dipath k-colouring, describing a homomorphism
model, and showing how to determine the 2-dipath chromatic number of tournaments
and bipartite tournaments. / Graduate
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/3277 |
| Date | 02 May 2011 |
| Creators | Young, Kailyn M. |
| Contributors | MacGillivray, Gary |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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