The donut-shop model of cops and robbers
| dc.contributor.advisor | Burgess, Andrea | |
| dc.contributor.advisor | Sankey, Alyssa | |
| dc.contributor.author | MacTavish, Evan Alexander | |
| dc.date.accessioned | 2024-02-08T15:12:02Z | |
| dc.date.available | 2024-02-08T15:12:02Z | |
| dc.date.issued | 2023-08 | |
| dc.description.abstract | We explore a variation of the game of Cops and Robbers on graphs, in which cops pursue a robber in the presence of one or more special vertices: donut-shops. The location of a donut-shop is determined before each player selects their starting position, and should a cop ever move to a donut-shop, they cannot move for the remainder of the game. These conditions form the donut-shop model for Cops and Robbers. This thesis introduces the donut-shop cop-number, representing the minimum number of cops needed to capture the robber in this model. We determine the donut-shop cop-number of some classes of graphs, which depends on the vertex on which the donut-shop is established. In particular, we give an upper bound for the donut-shop cop-number of planar graphs. A programmatic implementation of this model is also provided. | |
| dc.description.copyright | © Evan Alexander MacTavish, 2023 | |
| dc.format.extent | xi, 114 | |
| dc.format.medium | electronic | |
| dc.identifier.uri | https://unbscholar.lib.unb.ca/handle/1882/37692 | |
| dc.language.iso | en | |
| dc.publisher | University of New Brunswick | |
| dc.rights | http://purl.org/coar/access_right/c_abf2 | |
| dc.subject.discipline | Mathematics and Statistics | |
| dc.title | The donut-shop model of cops and robbers | |
| dc.type | master thesis | |
| oaire.license.condition | other | |
| thesis.degree.discipline | Mathematics and Statistics | |
| thesis.degree.grantor | University of New Brunswick | |
| thesis.degree.level | masters | |
| thesis.degree.name | M.Sc. |