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

## Synopsis

• Usage:
b = isForest G
b = isForest H
• Inputs:
• G, ,
• H, ,
• Outputs:
• b, , 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 .