Content deleted Content added
Cleaned up after move to mainspace. |
m Bolded title |
||
Line 1:
{{Short description|Method in combinatorics}}
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]] {{math|''H''}} on finite vertex set {{math|''V''}} with edge set {{math|''E''}} (i.e. a collection of subsets of {{math|''V''}} with some size constraints), what can we say about the [[independent set (graph theory)|independent sets]] of {{math|''H''}} (i.e. those subsets of {{math|''V''}} that contain no element of {{math|''E''}})? The hypergraph container lemma provides a method for tackling such questions.
| |||