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A guide to the Rado graph : exploring structural and logical properties of the Rado graph
Dissertation (MSc (Mathematics))--University of Pretoria, 2023.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2023
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| _version_ | 1867613521209982976 |
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| access_status_str | Open Access |
| author2 | Kellerman, Ruaan |
| author_browse | Kellerman, Ruaan |
| author_facet | Kellerman, Ruaan |
| collection | Thesis |
| dc_rights_str_mv | © 2022 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc (Mathematics))--University of Pretoria, 2023. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/89560 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:28.126Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/89560 A guide to the Rado graph : exploring structural and logical properties of the Rado graph Kellerman, Ruaan u16004231@tuks.co.za Michau, Michelle Rado graph Random graph Graph theory Model theory Definable sets UCTD Dissertation (MSc (Mathematics))--University of Pretoria, 2023. The Rado graph, denoted R, is the unique (up to isomorphism) countably infinite random graph. It satisfies the extension property, that is, for two finite sets U and V of vertices of R there is a vertex outside of both U and V connected to every vertex in U and none in V . This property of the Rado graph allows us to prove quite a number of interesting results, such as a 0-1-law for graphs. Amongst other things, the Rado graph is partition regular, non-fractal, ultrahomogeneous, saturated, resplendent, the Fra´ıss´e-limit of the class of finite graphs, a non-standard model of the first-order theory of finite graphs, and has a complete decidable theory. We classify the definable subgraphs of the Rado graph and prove results for finite graphs that satisfy a restricted version of the extension property. We also mention some parallels between the rationals viewed as a linear order and the Rado graph. Mathematics and Applied Mathematics MSc (Mathematics) Unrestricted 2023-02-15T09:47:14Z 2023-02-15T09:47:14Z 2023-04 2023 Dissertation * A2023 https://repository.up.ac.za/handle/2263/89560 10.25403/UPresearchdata.22096718 en © 2022 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | Rado graph Random graph Graph theory Model theory Definable sets UCTD A guide to the Rado graph : exploring structural and logical properties of the Rado graph |
| title | A guide to the Rado graph : exploring structural and logical properties of the Rado graph |
| title_full | A guide to the Rado graph : exploring structural and logical properties of the Rado graph |
| title_fullStr | A guide to the Rado graph : exploring structural and logical properties of the Rado graph |
| title_full_unstemmed | A guide to the Rado graph : exploring structural and logical properties of the Rado graph |
| title_short | A guide to the Rado graph : exploring structural and logical properties of the Rado graph |
| title_sort | guide to the rado graph exploring structural and logical properties of the rado graph |
| topic | Rado graph Random graph Graph theory Model theory Definable sets UCTD |
| url | https://repository.up.ac.za/handle/2263/89560 |