I'm reviewing an earlier exam with solutions by the professor. I found this:
Problem: Let G denote a simple, connected graph with n vertices and m edges. Translate the following statement to English and tell whether it is true or false.
∀v ∈ V(G) : δ(v) = 2 ⇒ G is Hamiltonian.
Solution: If the degree of each vertex is equal to 2, then G is Hamiltonian. True (because G is a cycle).
But how does the professor know that G is a cycle? Couldn't G contain two components? Is it a mistake?