This paper investigates ultrafilters in the context of connectivity systems, defined as pairs
$(X, f) $ where $ X $ is a finite set and $ f $ is a symmetric submodular function. Ultrafilters …

Graph characteristics are frequently examined using a variety of parameters, with ongoing
research focused on exploring these aspects. A fuzzy graph is a mathematical model in …

Linear-width is a well-known and highly regarded graph parameter. The concept of Single
Ideal and Linear obstacle serves as an obstruction to linear-width on a connectivity sysem …

A Fuzzy Graph extends classical graph theory by incorporating uncertainty, assigning a
membership degree to each edge. Tree-width [51, 52] is a fundamental measure that …

We prove a general width duality theorem for combinatorial structures with well-defined
notions of cohesion and separation. These might be graphs or matroids, but can be much …

We prove the existence of a computable function f∶ ℕ→ ℕ such that for every integer k and
every digraph D, either D contains a collection C of k directed cycles of even length such that …

In this thesis we describe dualities in directed as well as undirected graphs based on tools
such as width-parameters, obstructions and substructures. We mainly focus on directed …

In this thesis we adapt fundamental parts of the Graph Minors series of Robertson and
Seymour for the study of matching minors and investigate a connection to the study of …

A connected graph is one in which a path exists between any two vertices, ensuring that all
vertices are mutually accessible. Understanding how graph parameters behave under the …

This thesis concerns itself with two related topics: First, we discuss how the relatively
esoteric area of structural matching theory can be used to solve problems in more …