We are given a graph $G$:
After struggling for hours, I think it may be planar. If it is, I couldn't realize how to determine a proper drawing.
Things I've tried:
- Finding a subgraph isomorphic or homeomorphic to $K_5$ or $K_{33}$ (Since $K_{33}$ has no odd cycles I've tried removing them).
- Noted it has $8$ cycles of length $3$, $K_5$ has $10$. Maybe there is a way of obtaining the others that I'm not aware of).
- Obtaining a subgraph (with $|V|\geq3$) that has no cycles of length $3$ and $|E| > 2|V|-4$.
The question's been solved, but I couldn't help but post this more symmetric planar embedding