has.helly {HyperG} | R Documentation |
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 dmarchette@gmail.com
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)