Extends paper with: a notation section for color-class preimages; the
plane diamond coloring definition (4-coloring whose two classes lift to a
2-coloring of some BFS-rooted diamond scaffold); a connectedness lemma
for the scaffold; a proposition reformulating the property as parity-
separation of two color classes by BFS layers; a remark noting this is
strictly stronger than 4CT; and the conjecture that every maximal planar
graph admits such a coloring.
Adds plane_diamond_coloring.py with get_plane_diamond_scaffold and a
counterexample search that reduces the per-root check to 4-colorability
of an auxiliary graph forcing two colors onto opposite parity layers.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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