The bipartite ramsey number of cycles
| dc.contributor.author | Tivane, Amukelani | |
| dc.date.accessioned | 2023-11-21T09:29:05Z | |
| dc.date.available | 2023-11-21T09:29:05Z | |
| dc.date.issued | 2021 | |
| dc.description | A dissertation submitted in fulfilment of the requirements for the degree of Master of Science to the Faculty of Science, University of the Witwatersrand, Johannesburg, 2022 | |
| dc.description.abstract | The Ramsey number R(H1, H2) of two graphs H1 and H2 is the smallest positive integer n for which every red-blue coloring of the complete graph Kn of order n results in a subgraph of Kn isomorphic to H1 all of whose edges are colored red (called a red H1), or a subgraph of Kn isomorphic to H2 all of whose edges are colored blue (called a blue H2). The s-bipartite Ramsey number bs(H1, H2) of two bipartite graphs H1 and H2 is the smallest positive integer t, with t ≥ s, such that every red-blue coloring of the complete bipartite graph Ks,t results in a red H1 or a blue H2. For s = t, the sbipartite Ramsey number is known as the bipartite Ramsey number, which we denote by b(H1, H2). In this dissertation we investigate b(C2m, C2n) and bs(C2m, C2n) for m ≥ 2 and n ≥ 2. | |
| dc.description.librarian | PC(2023) | |
| dc.faculty | Faculty of Science | |
| dc.identifier.uri | https://hdl.handle.net/10539/37059 | |
| dc.language.iso | en | |
| dc.school | Mathematics | |
| dc.subject | Ramsey number | |
| dc.subject | s-bipartite Ramsey number | |
| dc.title | The bipartite ramsey number of cycles | |
| dc.type | Dissertation |