Graphs and Hypergraphs

Since the middle of the last century, Graph Theory has been an important tool in different fields, Iike Geometry, Algebra, Number Theory, Topology, Optimization, Operations Research, Median Algebras and so on. To solve new combinatorial problems, it was necessary to generalize the concept of a Graph.The notion of a “hypergraph” appeared around 1960 and one of the initial concerns was to extend some classical results of graph theory.Hypergraph Theory is an useful tool for discrete optimization Problems.A very good presentation of Graph and Hypergraph Theory is in C. Berge [442] and Harary [448].In this chapter, we have presented some important connections between Graph, Hypergraph Theory and Hyperstructure Theory.