2-dipath and proper 2-dipath k-colourings
| dc.contributor.author | Young, Kailyn M. | |
| dc.contributor.supervisor | MacGillivray, Gary | |
| dc.date.accessioned | 2011-05-02T22:05:50Z | |
| dc.date.available | 2011-05-02T22:05:50Z | |
| dc.date.copyright | 2011 | en_US |
| dc.date.issued | 2011-05-02 | |
| dc.degree.department | Dept. of Mathematics and Statistics | en_US |
| dc.degree.level | Master of Science M.Sc. | en_US |
| dc.description.abstract | 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. | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/3277 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights.temp | Available to the World Wide Web | en_US |
| dc.subject | graph theory | en_US |
| dc.subject | oriented graphs | en_US |
| dc.subject | tournaments | en_US |
| dc.title | 2-dipath and proper 2-dipath k-colourings | en_US |
| dc.title.alternative | Two-dipath and proper two-dipath k-colourings | en_US |
| dc.type | Thesis | en_US |