Gray code numbers of complete multipartite graphs
| dc.contributor.author | Bard, Stefan | |
| dc.contributor.supervisor | MacGillivray, Gary | |
| dc.date.accessioned | 2014-12-23T22:29:27Z | |
| dc.date.available | 2014-12-23T22:29:27Z | |
| dc.date.copyright | 2014 | en_US |
| dc.date.issued | 2014-12-23 | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science M.Sc. | en_US |
| dc.description.abstract | Let G be a graph and k be an integer greater than or equal to the chromatic number of G. The k-colouring graph of G is the graph whose vertices are k-colourings of G, with two colourings adjacent if they colour exactly one vertex differently. We explore the Hamiltonicity and connectivity of such graphs, with particular focus on the k-colouring graphs of complete multipartite graphs. We determine the connectivity of the k-colouring graph of the complete graph on n vertices for all n, and show that the k-colouring graph of a complete multipartite graph K is 2-connected whenever k is at least the chromatic number of K plus one. Additionally, we examine a conjecture that every connected k-colouring graph is 2-connected, and give counterexamples for k greater than or equal to 4. As our main result, we show that for all k greater than or equal to 2t, the k-colouring graph of a complete t-partite graph is Hamiltonian. Finally, we characterize the complete multipartite graphs K whose k-colouring graphs are Hamiltonian when k is the chromatic number of K plus one. | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/5815 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights.temp | Available to the World Wide Web | en_US |
| dc.rights.uri | http://creativecommons.org/publicdomain/zero/1.0/ | * |
| dc.subject | Graph Theory | en_US |
| dc.subject | Hamilton Cycle | en_US |
| dc.subject | Gray Code | en_US |
| dc.subject | Colouring Graph | en_US |
| dc.subject | Connectivity | en_US |
| dc.subject | Complete Multipartite | en_US |
| dc.title | Gray code numbers of complete multipartite graphs | en_US |
| dc.type | Thesis | en_US |