Exercise 0.1. Suppose that G is a finite graph all of whose vertices has degree two or greater. Prove that a cycle passes through each vertex. Conclude that G cannot be a tree.
The Attempt at a Solution
If every vertex in a graph G has degree two or greater, then there is always a way to get in and out without using the same edge. If we start at any vertex and try to traverse the graph by using the rule of getting in and out and not using the same edge, eventually we will realize that we can't stop, so this implies that there is a cycle. Therefore G can't be a tree.
I am new to this types of proofs, so I need feedback.