Problem
COM-B2-M07-P003 A Leaf in a Tree
#3
★★☆☆☆ Level 2 of 5
Prove that every tree with at least two vertices has at least two leaves.
Take a longest path.
Choose a longest simple path in the tree. If an endpoint has a neighbour outside the path, the path can be extended. If it is adjacent to another vertex of the path besides its neighbour on the path, a cycle appears. Hence its degree is \(1\). The same holds for the other endpoint. Thus there are two leaves.
This is a stronger version of the basic leaf fact.