Container method

rdf:langString Container method

rdf:langString The method of (hypergraph) containers is a powerful tool that can help characterize the typical structure and/or answer extremal questions about families of discrete objects with a prescribed set of local constraints. Such questions arise naturally in extremal graph theory, additive combinatorics, discrete geometry, coding theory, and Ramsey theory; they include some of the most classical problems in the associated fields. These problems can be expressed as questions of the following form: given a hypergraph H on finite vertex set V with edge set E (i.e. a collection of subsets of V with some size constraints), what can we say about the independent sets of H (i.e. those subsets of V that contain no element of E)? The hypergraph container lemma provides a method for tackling such questions.