An original five-cycle coloring puzzle. Alternating two colors around an odd cycle leaves a conflict; a third color fixes this example. Check all five edges. This small case is easy and is not a proof of general hardness. General graph 3-colorability is NP-complete; a polynomial-time algorithm for all input graphs would resolve P vs NP. No claim that every instance is hard or every algorithm must enumerate all assignments.
Sources read on 19 October 2026: (listed unsolved)
UBC CS320 handout:
Original diagram, script and authored English captions. Synthetic narration: Jenny. #PvsNP #GraphColoring #Mathematics
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