Rotation sequences and edge-colouring of binary tree pairs

AbstractThe famous four-colour problem of planar maps is equivalent, by an optimally fast reduction, to the problem of colouring pairs of binary trees (CPBT). Extant proofs of the four colour theorem lack conciseness, are not lucid in their detail and require hours of electronic computation. The search for a more satisfactory proof continues and, in this spirit, we explore one approach to CPBT based upon the rotation operation in binary trees. We prove that a more satisfactory proof exists if a rotational path between the two trees of every problem instance satisfies our non-colour-clashing sequence conjecture