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Helly family

In combinatorics, a Helly family of order k is a family of sets in which every minimal subfamily with an empty intersection has k or fewer sets in it. Equivalently, every finite subfamily such that every k-fold intersection is non-empty has non-empty total intersection. The k-Helly property is the property of being a Helly family of order k.

Helly dimension, The Helly property in hypergraphs & Examples

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Examples

Formal definition

Helly dimension

The Helly property

The Helly property in hypergraphs

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Helly family

Nodes40
Edges39
Triples21
Avg. degree1.95
Density0.05
Components1

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Helly family

Top relations

related to Examples · 10
Helly family → Chinese, Helly, In, It, Let, That, The, Then, Therefore, Thus
related to Helly dimension · 6
Helly family → Euclidean, For, Helly, Helly's, If, The Helly
related to The Helly property · 3
Helly family → Helly, If, The
related to Formal definition · 2
Helly family → Helly, More

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Important terminology

helly family property intersection empty every dimension order sets number subfamily space hypergraph minimal finite intervals set euclidean less two

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Helly familyrelated to ExamplesIn0.60section
Helly familyrelated to ExamplesTherefore0.60section
Helly familyrelated to ExamplesIt0.60section
Helly familyrelated to ExamplesHelly0.60section
Helly familyrelated to ExamplesLet0.60section
Helly familyrelated to ExamplesThen0.60section
Helly familyrelated to ExamplesThus0.60section
Helly familyrelated to ExamplesThe0.60section
Helly familyrelated to ExamplesThat0.60section
Helly familyrelated to ExamplesChinese0.60section
Helly familyrelated to Formal definitionMore0.60section
Helly familyrelated to Formal definitionHelly0.60section

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