Acyclic Colouring of Graphs on Surfaces
| dc.contributor.author | Redlin, Shayla | |
| dc.date.accessioned | 2018-09-04T20:29:17Z | |
| dc.date.available | 2018-09-04T20:29:17Z | |
| dc.date.issued | 2018-09-04 | |
| dc.date.submitted | 2018-08-28 | |
| dc.description.abstract | An acyclic k-colouring of a graph G is a proper k-colouring of G with no bichromatic cycles. In 1979, Borodin proved that planar graphs are acyclically 5-colourable, an analog of the Four Colour Theorem. Kawarabayashi and Mohar proved in 2010 that "locally" planar graphs are acyclically 7-colourable, an analog of Thomassen's result that "locally" planar graphs are 5-colourable. We say that a graph G is critical for (acyclic) k-colouring if G is not (acyclically) k-colourable, but all proper subgraphs of G are. In 1997, Thomassen proved that for every k >= 5 and every surface S, there are only finitely many graphs that embed in S that are critical for k-colouring. Here we prove the analogous result that for each k >= 12 and each surface S, there are finitely many graphs embeddable on S that are critical for acyclic k-colouring. This result implies that there exists a linear time algorithm that, given a surface S and large enough k, decides whether a graph embedded in S is acyclically k-colourable. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/13732 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | graph theory | en |
| dc.subject | graph colouring | en |
| dc.subject | acyclic colouring | en |
| dc.subject | colouring graphs on surfaces | en |
| dc.subject | critical graphs | en |
| dc.title | Acyclic Colouring of Graphs on Surfaces | en |
| dc.type | Master Thesis | en |
| uws-etd.degree | Master of Mathematics | en |
| uws-etd.degree.department | Combinatorics and Optimization | en |
| uws-etd.degree.discipline | Combinatorics and Optimization | en |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws.contributor.advisor | Postle, Luke | |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |