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Cycle decompositions and t-perfect graphs
(Universität Ulm, 2017-10-18)
The thesis is divided into two parts. The first part deals with t-perfect graphs. A graph is called t-perfect if its stable set polytope is fully described by non-negativity, edge and odd-cycle constraints. We give ...
Exponential domination, exponential independence, and the clustering coefficient
(Universität Ulm, 2017-11-22)
This dissertation contains four research papers. The first two papers are about exponential domination in graphs, which is a variant of domination in graphs. In the first paper, we show results about the corresponding ...
Domination and forcing
(Universität Ulm, 2018-02-07)
This thesis comprises the results of five research papers on domination and zero forcing. In "Largest Domination Number and Smallest Independence Number of Forests with given Degree Sequence" (Gentner, Henning, Rautenbach, ...
On problems related to graph colouring
(Universität Ulm, 2017-11-24)
In this thesis we study various problems from the prominent area of graph colourings. We provide a characterisation of t-perfect triangulations and quadrangulations of the projective plane. For the latter class, a novel ...