Schäfer, Philipp Matthias
FacultiesFakultät für Mathematik und Wirtschaftswissenschaften
LicenseCC BY-SA 3.0 Deutschland
This thesis primarily gives an overview of research on so called betweenness relations with a focus on own contributions to that subject. Betweenness relations represent a generalisation of the geometric notion that one point can lie between two others. Formally, a betweenness relation is a set of triples such that it contains the triple $(a,b,c)$ if and only if it contains the triple $(c,b,a)$. An overview over results on characterisations of betweenness relations that are induced by various mathematical structures is given. This is followed by algorithmic considerations on recognizing special subsets of betweenness relations. Finally, results related to abstract convexity problems - path convexity and conversion processes - are presented. Though they do not fit perfectly to the previous results, they are products of research conducted with my colleagues during the last three years.
Subject HeadingsGraphentheorie [GND]
Betweenness relations (Mathematics) [LCSH]
Convex domains [LCSH]
Graph theory [LCSH]