Namespaces
Variants
Actions

Helly number

From Encyclopedia of Mathematics
Jump to: navigation, search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

$ \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