1 This question is about the planar graph shown below.
\includegraphics[max width=\textwidth, alt={}, center]{cc58fb7a-efb6-4548-a8e1-e40abe1eb722-2_567_1317_395_374}
- Apply Kuratowski's theorem to verify that the graph is planar.
- Use Euler's formula to calculate the number of regions in a planar representation of the graph.
- Write down a Hamiltonian cycle for the graph.
- By finding a suitable pair of vertices, show that Ore's theorem cannot be used to prove that the graph, as shown above, is Hamiltonian.
- Draw the graph formed by using the contractions AB and CF .
- Use Ore's theorem to show that this contracted graph is Hamiltonian.