Reformulating the Map Color Theorem

Abstract

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.