Colouring Cayley Graphs
| dc.contributor.author | Chu, Lei | en |
| dc.date.accessioned | 2006-08-22T14:21:57Z | |
| dc.date.available | 2006-08-22T14:21:57Z | |
| dc.date.issued | 2005 | en |
| dc.date.submitted | 2005 | en |
| dc.description.abstract | We will discuss three ways to bound the chromatic number on a Cayley graph. 1. If the connection set contains information about a smaller graph, then these two graphs are related. Using this information, we will show that Cayley graphs cannot have chromatic number three. 2. We will prove a general statement that all vertex-transitive maximal triangle-free graphs on <i>n</i> vertices with valency greater than <i>n</i>/3 are 3-colourable. Since Cayley graphs are vertex-transitive, the bound of general graphs also applies to Cayley graphs. 3. Since Cayley graphs for abelian groups arise from vector spaces, we can view the connection set as a set of points in a projective geometry. We will give a characterization of all large complete caps, from which we derive that all maximal triangle-free cubelike graphs on 2<sup>n</sup> vertices and valency greater than 2<sup>n</sup>/4 are either bipartite or 4-colourable. | en |
| dc.format | application/pdf | en |
| dc.format.extent | 342392 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/10012/1125 | |
| dc.language.iso | en | en |
| dc.pending | false | en |
| dc.publisher | University of Waterloo | en |
| dc.rights | Copyright: 2005, Chu, Lei. All rights reserved. | en |
| dc.subject | Mathematics | en |
| dc.subject | Cayley graphs | en |
| dc.subject | codes | en |
| dc.subject | projective geometry | en |
| dc.title | Colouring Cayley Graphs | en |
| dc.type | Master Thesis | en |
| uws-etd.degree | Master of Mathematics | en |
| uws-etd.degree.department | Combinatorics and Optimization | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |
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