How do you prove that this graph is or isn't planar? Euler's inequality is correct here. It seems like there is a $K_{3,3}$ subgraph, but I can't find it. How can I check whether this graph is planar or not?
2026-03-26 17:29:28.1774546168
Prove that this graph is planar
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One crude drawing deserves another.
In general if you are trying to find if a graph is planar or not, you first start playing around trying to find a $K_{3,3}$ or $K_5$ subgraph (or minor). If you struggle to find one, the graph might be planar, so then you play around trying to find a planar embedding. Alternate these two methods of playing accordingly until something gives.