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, essential in …

This paper explores two fundamental concepts: branch width and weak ultrafilter. Branch
width is a significant graph width parameter that measures the degree of connectivity in a …

Tangle, a concept related to graph width parameters, has been defined and studied in graph
theory. It has a dual relationship with branch width. Loose Tangle relaxes the axioms of …

Graph characteristics are often analyzed using various parameters, with ongoing research
dedicated to exploring these aspects. A filter is a fundamental concept in mathematics …

The exploration of graph width parameters, spanning both graph theory and algebraic
frameworks, has captured substantial attention. Among these, branch width has distinctly …

Algorithmicists are well-aware that fast dynamic programming algorithms are very often the
correct choice when computing on compositional (or even recursive) graphs. Here we …

The Latin aphorism 'divide et impera'conveys a simple, but central idea in mathematics and
computer science:'split your problem recursively into smaller parts, attack the parts, and …

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 …

The study of graph width parameters is a well-established field within graph theory.
Recently, numerous researchers have been actively extending undirected width parameters …

The field of undirected graph parameters is a very huge one and has been wellresearched
since the 1980s. A graph parameter, also called width measure, is a function that associates …