Hypergraphs: Combinatorics of Finite Sets

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Elsevier, 1 may 1984 - 254 páginas
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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Índice

Chapter 1 General concepts
1
Chapter 2 Transversal sets and matchings
43
Chapter 3 Fractional transversals
74
Chapter 4 Colourings
115
Chapter 5 Hypergraphs generalising bipartite graphs
155
Matching and colourings in matroids
217
References
237
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