Hypergraphs

Rating:
Summary: The bible of hypergraphs
Review: 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.

Rating:
Summary: The bible of hypergraphs
Review: 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.