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.
Contents
1. General Concepts. Dual Hypergraphs. Degrees. Intersecting Families. The Coloured Edge Property and Chvátal's
Conjecture. The Helly Property. Section of a Hypergraph and the Kruskal-Katona Theorem. Conformal Hypergraphs. Representative Graphs.
2. Transversal Sets and Matchings. Transversal Hypergraphs. The Coefficients r and r'. r-Critical Hypergraphs. The König
Property.
3. Fractional Transversals. Fractional Transversal Number. Fractional Matching of a Graph. Fractional Transversal
Number of a Regularisable Hypergraph. Greedy Transversal Number. Ryser's Conjecture. Transversal Number of Product Hypergraphs.
4.
Colourings. Chromatic Number. Particular Kinds of Colourings. Uniform Colourings. Extremal Problems Related to the Chromatic
Number. Good Edge-Colourings of a Complete Hypergraph. An Application to an Extremal Problem. Kneser's Problem.
Books and book related electronic products are priced in US dollars (USD), euro (EUR), and Great Britain Pounds (GBP). USD prices apply to the Americas and Asia Pacific. EUR prices apply in Europe and the Middle East. GBP prices apply to the UK and all other countries.
Home | Elsevier Sites | Privacy Policy | Terms and Conditions | Feedback | Site Map | A Reed Elsevier Company