Is it possible to have a planar graph with two edge-disjoint Hamiltonian cycles?
2026-03-27 13:46:58.1774619218
Edge-disjoint Hamiltonian cycles in a planar graph.
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Yes. Here is an example on the octahedron. It is easy to see that this is the smallest possible example, since if $G$ has fewer than $6$ vertices, or $6$ vertices with fewer edges, there aren't enough edges for two separate Hamilton cycles.