Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.578559
Title: Combinatorial embeddings and representations
Author: Psomas, Constantinos
Awarding Body: Open University
Current Institution: Open University
Date of Award: 2011
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Abstract:
Topological embeddings of complete graphs and complete multipartite graphs give rise to combinatorial designs when the faces of the embeddings are triangles. In this case, the blocks of the design correspond to the triangular faces of the embedding. These designs include Steiner, twofold and Mendelsohn triple systems, as well as Latin squares. We look at construction methods, structural properties and other problems concerning these cases. In addition, we look at graph representations by Steiner triple systems and by combinatorial embecldings. This is closely related to finding independent sets in triple systems. We examine which graphs can be represented in Steiner triple systems and combinatorial embeddings of small orders and give several bounds including a bound on the order of Steiner triple systems that are guaranteed to represent all graphs of a given maximum degree. Finally, we provide an enumer- ation of graphs of up to six edges representable by Steiner triple systems.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.578559  DOI: Not available
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