Graph Theory Question

I need help with the following proof

Let G Be a graph in which every vertext has degree

atleast 2. Prove that G contains a cycle (Hint Imagine

walking along hte graph, will you ever get ato a dead vertex,

if not, what must evedntually happen.

### 1 Answer | Add Yours

Proof

Begin at vertex A. There are at least two paths to choose from; choose one at random. This process continues (you never get to a dead end because there are no vertices of degree 1) until you have either (i) visited all vertices in the graph or (ii) traversed a cycle. In case (i), the next path you choose will result in a cycle, so your graph must contain a cycle. QED!

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes