Helly number
From Encyclopedia of Mathematics
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$ \def\X{\mathcal X} % family of sets \def\S{\mathcal S} % subfamily $
The Helly number $ H(\X) $ of a family of sets $\X$ is (in analogy to Helly's theorem) the smallest natural number $k$ such that the following (compactness-type) intersection property holds:
- Let $ \S $ be a subfamily of $ \X $. If any $k$ members of $\S$ have a common point, then the sets of $\S$ have a common point.
This is also called the Helly property, and the corresponding is called a Helly family (of order $k$).
How to Cite This Entry:
Helly number. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Helly_number&oldid=30988
Helly number. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Helly_number&oldid=30988