Forest

This article defines a property that can be evaluated to true/false for any undirected graph, and is invariant under graph isomorphism. Note that the term "undirected graph" as used here does not allow for loops or parallel edges, so there can be at most one edge between two distinct vertices, the edge is completely described by the vertices it joins, and there can be no edge from a vertex to itself.
View other such properties

Definition

An undirected graph is termed a forest or acyclic graph if it satisfies the following equivalent conditions:

1. It has no subgraph isomorphic to a cycle graph of size three or more
2. All its connected components are trees, i.e., it is a vertex-disjoint union of trees
3. Its girth is $\infty$

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
tree

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
triangle-free graph