On the achromatic number of graphs
| dc.contributor.author | Hughes, Frederick John | en_US |
| dc.date.accessioned | 2024-08-14T17:26:07Z | |
| dc.date.available | 2024-08-14T17:26:07Z | |
| dc.date.copyright | 1994 | en_US |
| dc.date.issued | 1994 | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science M.Sc. | en |
| dc.description.abstract | The achromatic number of a graph G 1s the largest number of colours that can be assigned to the vertices of G so that (1) adjacent vertices are assigned different colours, and (n) any two different colours are assigned to some pair of adjacent vertices. This thesis contributes to the study of the achromatic number by outlining the research since 1967. The effects on the achromatic number of several different operat10ns are surveyed, including that of the categorical product. The bounds on the achromatic numb er of paths, cycles, k-regular graphs and trees are then investigated, followed by an exploration of the relationship between clique number and achromatic number. Various results on n-minimal graphs are also reviewed. Finally, results concerning the computational complexity of the achromatic number problem for arbitrary and restricted graphs are presented. Included in this thesis are proofs of some theorems which illustrate an important technique or idea. Several original results are given, including n-minimal graph and Nordhaus-Gaddum type problems. | en |
| dc.format.extent | 66 pages | |
| dc.identifier.uri | https://hdl.handle.net/1828/18243 | |
| dc.rights | Available to the World Wide Web | en_US |
| dc.title | On the achromatic number of graphs | en_US |
| dc.type | Thesis | en_US |
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