even_level: title/abstract/intro -- frame conjecture as stronger than the 4CT

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Retitle to "Even Level Graph Generators: a constructive conjecture
stronger than the Four Color Theorem" and state explicitly in the
abstract and introduction that the conjecture implies the four color
theorem but is strictly stronger: a 4-coloring grouped {1,2}|{3,4} is
exactly a partition into two bipartite-inducing parts, so 4CT is the bare
existence of such a partition, whereas the conjecture demands it be
realized constructively (bridge-switch level parity, or two induced
trees). Hence a proof is a new constructive proof of 4CT, and the
conjecture is at least as hard -- very likely harder.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

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2026-05-22 16:22:15 -04:00

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papers/even_level_graph_generators/paper.pdf

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