1 - 7 of 7 Chapters
[View the significant developments of combinatoric thanks to computer science [And89, LW01], hypergraphs are increasingly important in science and engineering. Hypergraphs are a generalization of graphs, hence many of the definitions of graphs carry verbatim to hypergraphs. In this chapter we...
[In the first chapter we saw that hypergraphs generalize standard graphs by defining edges between multiple vertices instead of only two vertices. Hence some properties must be a generalization of graph properties In this chapter, we introduce some basic properties of hypergraphs which will be...
[The main problems in combinatorics are often related in the concept of coloring [CGL95a, CGL95b]. Hypergraph colorings is a well studied problem in the literature in combinatorics [Lov73]. Colorations have many applications in telecommunication, computer science and engineering. Unlike the...
[Roughly speaking we introduced the more important concepts about hypergraphs, we will see a little bit more in the next chapters, but there are very important classes of hypergraphs. This chapter introduces some particular hypergraphs which either have good properties, or are very important for...
[In many human activities we must first model. The choice of a good model is essential in order to be able to deal with the complexity of the phenomena we need to understand. The objects we want to represent use increasingly more data: large databases, satellite images, large clusters, ...]
[Outside the classical theory of hypergraphs, there is a beginning of theory which is not yet stabilized, it is the theory of directed hypergraphs. This chapter investigates the notion of directed hypergraph (dirhypergraph). We try to clarify its vocabulary.]
[Like in most fruitful mathematical theories, the theory of hypergraphs has many applications. Hypergraphs model many practical problems in many different sciences. it makes very little time (20 years) that the theory of hypergraphs is used to model situations in the applied sciences. We find...
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