014-2004

MO640 - Multiple-choice question

Consider a simple, connected graph composed solely by two cycles that share exactly one vertex, in a format that resembles a bow tie. Which if the following statements is true?

1. This graph is not Eulerian or Hamiltonian.
2. This graph is Eulerian, but not Hamiltonian.
3. This graph is Hamiltonian, but not Eulerian.
4. This graph is both Eulerian and Hamiltonian.
5. None of the above

Original idea by: José Augusto Amgarten Quitzau