Investigations into the Universal Algebra of Hypergraph Coverings and Applications
Julian Bitterlich · TUbilio (Technical University of Darmstadt) · 2019
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.