Development of Hypergraph Theory

Аннотация

In recent decades, the theory of hypergraphs has been applied to real-life problems. The tools of hypergraph theory can be used for modeling networks, biological networks, data structures, scheduling processes and computations, and many other systems with complex relationships between the entities. From the theoretical point of view, hypergraphs make it possible to generalize certain theorems in graph theory or even replace a number of theorems on graphs by one theorem on hypergraphs. However, the majority of the potentials in the development of hypergraph theory are blocked due to inconsistencies in the basic terms. It is proposed to make up a list of basic terms related to hypergraph theory, which can help standardize this theory.