Hypergraphs: Combinatorics of Finite Sets (Volume 45) (North-Holland Mathematical Library, Volume 45) 1st Edition by C. Berge (PDF)

Description

Graph Theory has proved to be an extremely useful tool for solving combinatorial problems in such diverse areas as Geometry, Algebra, Number Theory, Topology, Operations Research and Optimization. It is natural to attempt to generalise the concept of a graph, in order to attack additional combinatorial problems. The idea of looking at a family of sets from this standpoint took shape around 1960. In regarding each set as a “generalised edge” and in calling the family itself a “hypergraph”, the initial idea was to try to extend certain classical results of Graph Theory such as the theorems of Turán and König. It was noticed that this generalisation often led to simplification; moreover, one single statement, sometimes remarkably simple, could unify several theorems on graphs. This book presents what seems to be the most significant work on hypergraphs.

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Editorial Reviews: Review This book presents what seems to be the most significant work on hypergraphs.L’Enseignement Mathematique

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Not to be confused Graphs and Hypergraphs (another of his books), Claude Berge’s Hypergraphs focuses solely on the structures also known as “set systems”. For the curious, a hypergraph consists of a set V and a set E of subsets of S. A graph is a special case of a hypergraph where each element of E has cardinality two.Published in 1989, this book has become, by default, the authoritative text on hypergraphs. It does not delve into more advanced, technical results (e.g.: asymptotics, etc…) but instead covers all the fundamental material related to hypergraphs (e.g.: Helly property, Konig property, Kruskal-Katona, etc…). Since hypergraphs are usually not part of standard curricula, this book has definitely carved out its own niche. Practically every paper which mentions hypergraphs (written since 1989) references it.This book appears to be written for practicing mathematicians (or sufficiently sophisticated students) who have stumbled upon a combinatorial problem and are in need of some basic (though non-obvious) results. Thus, in many cases, results are presented somewhat tersely and with little context or motivation with the implicit assumption that the reader already knows what hypergraphs are good for and is skillful enough to navigate the densely packed theorems.

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