isForest -- determines whether a (hyper)graph is a forest

Synopsis

Usage:

b = isForest G

b = isForest H
Inputs:
- G, a graph,
- H, a hypergraph,
Outputs:
- b, a Boolean value, true if G (or H) is a forest

Description

This function determines if a graph or hypergraph is a forest. A graph is a forest if if the graph has no cycles. We say that a hypergraph is forest if each connected component is a tree in the sense of S. Faridi. See the paper "The facet ideal of a simplicial complex," Manuscripta Mathematica 109, 159-174 (2002).

i1 : S = QQ[a..f];

i2 : t = graph {a*b,a*c,a*e}

o2 = Graph{"edges" => {{a, b}, {a, c}, {a, e}}}
           "ring" => S
           "vertices" => {a, b, c, d, e, f}

o2 : Graph

i3 : isForest t

o3 = true

i4 : h = hyperGraph {a*b*c,c*d*e,b*d*f}

o4 = HyperGraph{"edges" => {{a, b, c}, {c, d, e}, {b, d, f}}}
                "ring" => S
                "vertices" => {a, b, c, d, e, f}

o4 : HyperGraph

i5 : isForest h

o5 = false

Ways to use isForest :

isForest(Graph)
isForest(HyperGraph)

For the programmer

The object isForest is a method function.