# Is it possible for a graph that has a hamiltonian circuit but no a eulerian circuit

Definitions of both:

Hamiltonian Circuit: Visits each vertex exactly once and consists of a cycle. Starts and ends on same vertex.

Eulerian Circuit: Visits each edge exactly once. Starts and ends on same vertex.

Is it possible a graph has a hamiltonian circuit but not an eulerian circuit?

Here is my attempt based on proof by contradiction:

Suppose there is a graph G that has a hamiltonian circuit. That means every vertex has at least one neighboring edge. <-- stuck

Another example: the complete graph on $n$ vertices, when $n$ is even.
The theta graph: $\Theta$. Four more characters to be postable.