4 The graph below connects nine vertices A, B, ..., H, I.
\includegraphics[max width=\textwidth, alt={}, center]{9fe422a0-c498-4ad5-bdfc-f70482960d39-3_543_693_1347_680}
- (a) Show that the minimum sum of the degrees of each pair of non-adjacent vertices is 9 .
(b) Explain what you can deduce from the result in part (a). - Use Kuratowski's theorem to prove that the graph is non-planar.
- Prove that there is no subgraph of the graph that is isomorphic to \(\mathrm { K } _ { 4 }\), without using subdivision or contraction.