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Every biconnected 3-regular graph with n vertices has O(2 n/2) 3-edge-colorings; all of which can be listed in time O(2 n/2) (somewhat slower than the time to find a single coloring); as Greg Kuperberg observed, the graph of a prism over an n/2-sided polygon has Ω(2 n/2) colorings (lower instead of upper bound), showing that this bound is ...