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Reformulating the Map Color Theorem
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This paper discusses reformulations of the problem of coloring plane maps with four colors. The context is the edge-coloring with three colors of cubic graphs such that three distinct colors occur at each vertex. We include discussion of the Eliahou-Kryuchkov conjecture, the Penrose formula, the vector cross product formulation and the reformulations in terms of formations and factorizations due to G. Spencer-Brown. The latter includes a proof of the Spencer-Brown parity lemma and discussion of the parity-pass algorithm.
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A counterexample for the polar conjecture of Spencer-Brown
A plane graph with a non-polar pentagonal face makes Spencer-Brown's parity pass return to its initial coloring after 60 steps, disproving his Polar Conjecture.
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