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This work aims to provide an independent verification of a counterexample to Goemans' conjecture regarding unsplittable flows.

July 27, 2026Open Access

An independent exact verification of the 2026 counterexample to Goemans' unsplittable-flow cost conjecture, with the violation constant it forces

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Independent verification of the Goemans' conjecture counterexample, indicating a fundamental flaw in a key theorem.

This work aims to provide an independent verification of a counterexample to Goemans' conjecture regarding unsplittable flows.
Exact rational enumeration was performed without external verification tools.
The instance was re-entered manually for verification accuracy.
Computational results were documented to ensure reproducibility.
The counterexample confirms that Goemans' conjecture is false, forcing a violation of exactly 16/15 of the maximum demand.
All previously proved results in the area survived testing on the counterexample.
An optimal separator for the graph was identified, indicating no cost improvement is possible through reweighting.

Felipe Santibañez-Leal (2026) studied this question.

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