has.helly {HyperG}

Helly Property

Description

Check whether a hypergraph has the Helly property.

Usage

has.helly(h, strong=FALSE)
is.helly(h)

Arguments

h

a hypergraph.

strong

logical.

Details

An intersecting family is a collection of hyper-edges such that the intersection of any pair of hyper-edges in the family is non-empty. A hypergraph has the Helly property if each intersecting family has a non-empty intersection – there is at least one vertex in every hyper-edge. This is an implementation of the algorithm on page 32 of Bretto. The argument strong indicates whether the test should be for the strong Helly property or not. A hypergraph has the strong Helly property if every partial induced sub-hypergraph has the Helly property.

The function is.helly is an alias for a check for the non-strong Helly property.

Value

a logical.

Note

Have not yet implemented the strong Helly property algorithm.

Author(s)

David J. Marchette [e-mail]

References

Bretto, Alain, Hypergraph theory, An introduction. Springer, 2013.

Examples

	## Example from Bretto
	h <- hypergraph_from_edgelist(list(1:5,
	          c(2,4,6,7),
				 c(4:6,8,9),
				 9:10))
   has.helly(h)