How to Not Prove Two Important Theorems
summary
Proposes an approach that amplifies a small-error 3‑edge‑coloring into a full counterexample and proves a reduction showing that an algorithm that colors bridgeless cubic planar graphs with o(n) errors would yield the four‑color result, using amplifier gadgets built with planarity and duality and actually working for several constructions. Solves a related two‑line permutation problem by computing cycle parity via a formula — parity via inversion count — but the analogous three‑line case resists. Introduces an unordered‑pair graph product and reports partial structural facts without a complete solution.
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