Balanced Hypergraphs and Some Applications to Graph Theory

Publisher Summary This chapter provides an overview of the combinatorial properties of a special kind of hypergraphs, called the balanced hypergraphs, which provide new theorems of graph theory. A hypergraph consists of a finite set X of n vertices together with a family of m nonempty subsets of X, called the edges. A graph is made up of vertices or nodes and lines called edges that connect them. A graph can be undirected, that is, there is no distinction between the two vertices associated with each edge, or its edges can be directed from one vertex to another; Graphs are one of the prime objects of study in discrete mathematics.