definition: forest
an acyclic graph is called a forest.
(taken from Reinhard Diestel, 2017 chapter 1.5 trees and forests)
definition: spanning forest
a forest of is a spanning forest if every pair of vertices that are connected in are also connected in . a spanning forest that is a tree is called a spanning tree.
(taken from Philip N. Klein and Shay Mozes, 2024 chapter 3.1 spanning forests and trees)
definition: tree edge
let be spanning forest of . an edge of is a tree edge with respect to if belongs to , and otherwise is a nontree edge.
(taken from Philip N. Klein and Shay Mozes, 2024 chapter 3.1 spanning forests and trees)