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 …

In graph theory, the hypergraph [22] extends the traditional graph structure by allowing
edges to connect multiple vertices, and this concept is further broadened by the …

There exist complex patterns behind the decision-making processes of different individuals
across different environments. For instance, in a social recommender system, various user …

Graph theory, a branch of mathematics, studies the relationships between entities using
vertices and edges. Uncertain Graph Theory has emerged within this field to model the …

Set theory, a fundamental branch of mathematics, focuses on the study of" sets," or
collections of objects. To address real-world uncertainties more effectively, various …

Classical graph classes include undirected graphs, where edges lack orientation, and
directed graphs, where edges have specific directions. Recently, concepts such as …

Graph theory, a fundamental branch of mathematics, examines relationships between
entities through the use of vertices and edges. Within this field, Uncertain Graph Theory has …

In contrast to undirected width measures such as tree-width, which have provided many
important algorithmic applications, analogous measures for digraphs such as directed tree …

Entanglement is a parameter for the complexity of finite directed graphs that measures to
what extent the cycles of the graph are intertwined. It is defined by way of a game similar in …

In contrast to undirected width measures (such as tree-width or clique-width), which have
provided many important algorithmic applications, analogous measures for digraphs such …