(1) Prove that the Groetzsch Graph is not planar.
2026-03-28 05:20:40.1774675240
Groetzsch Graph planarity
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For (1) recall that a graph is non-planar if and only if it contains a subgraph that is a subdivision of either $K_5$ or $K_{3,3}$. So can you find such a subgraph? (Hint: $K_5$ works for this case).
Something seems to be wrong with (2). Consider three "countries" where each two share a border (e.g., Oregon, Nevada and California). You clearly need three colors.