A forest is an undirected graph in which any two vertices are connected by at most one path.

Equivalently, a forest is an undirected graph with no cycles, all of whose connected components are trees; in other words, the graph consists of a disjoint union of trees.

Theorem: A graph is a forest if and only if each pair of distinct edges there’s only one path from to .

Theorem: A forest with vertices and components has edges.