Bitterlich, Julian (2019):
Investigations into the Universal Algebra of Hypergraph Coverings and Applications.
Darmstadt, Technische Universität,
[Ph.D. Thesis]
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Phd thesis Julian Bitterlich -
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Item Type: | Ph.D. Thesis | ||||
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Title: | Investigations into the Universal Algebra of Hypergraph Coverings and Applications | ||||
Language: | English | ||||
Abstract: | This thesis deals with two topics: acyclic covers and extension problems. The first part of the thesis deals with unbranched covers of graphs. The general theory of unbranched covers is discussed and then generalized to granular covers. Covers of this type maintain fixed structures of the covered graph. It is shown how unbranched covers of hypergraphs can be reduced to granular covers. With the help of further results we can identify the class of hypergraphs that have acyclic unbranched covers. The second part of the paper deals with extension problems. An extension problems it is about finitely extending finite structures so that partial automorphisms of the initial structure can be completed on the extension. We discuss classical results and reformulate them so that they are suitable for an algebraic characterization. These can be used to get new results regarding extension problems. |
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Place of Publication: | Darmstadt | ||||
Classification DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik | ||||
Divisions: | 04 Department of Mathematics > Logic > Algorithmic Model Theory > Model Constructions and Decompositions | ||||
Date Deposited: | 20 May 2019 13:19 | ||||
Last Modified: | 09 Jul 2020 02:36 | ||||
URN: | urn:nbn:de:tuda-tuprints-86914 | ||||
Referees: | Otto, Prof. Dr. Martin and Auinger, Dr. Karl and Michael, Prof. Dr. Joswig | ||||
Refereed: | 12 February 2019 | ||||
URI: | https://tuprints.ulb.tu-darmstadt.de/id/eprint/8691 | ||||
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