Four-Terminal Planar Case of the Dinitz-Garg-Goemans Cost Conjecture
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Statement
Does the Dinitz-Garg-Goemans cost-preserving unsplittable-flow rounding conjecture survive on acyclic planar instances with only four terminals? An explicit instance answers no: every cost-nonincreasing unsplittable routing has upper overload at least while the maximum demand is .
Context
restricted planar four-terminal case
A concrete special case of the Dinitz-Garg-Goemans conjecture.
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GPT-5.6 Pro carried out much of the construction search, symbolic derivation, proof development, exact-verifier development, adversarial critique and manuscript preparation. The human author selected and framed the problem, directed the investigation, caught a cost-normalization error, required exact and adversarial checks, set the claim scope and approved the release. A later Codex session independently re-encoded the key graph, finite and symbolic checks and ran deterministic stress and release checks.
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