Problem
COM-B1-M12-P020 Set 5. Leaves
#20
★★★☆☆ Level 3 of 5
Prove that a tree with at least two vertices has at least two vertices of degree \(1\).
Take a longest simple path.
The endpoints of a longest simple path cannot have additional neighbors: otherwise the path could be extended or a cycle would appear. Hence both endpoints have degree \(1\).
Graph lemma in short form.