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# “Dinitz-Garg-Goemans conjecture is false.”

Dmitry Rybin (@DmitryRybin1), X, 2026-07-22.
Source: https://x.com/DmitryRybin1/status/2079904005652893709

## Archived text

> Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years.
> 
> The graph below has fractional flow cost 58. Any unsplittable flow (with capacity violation <=15) has cost at least 60.
> 
> Chat with GPT 5.6 Pro where this was found: https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de063

Archived 2026-10-19 via fxtwitter (unofficial).
Counts: 4,877,622 views, 9,981 likes, 923 reposts, 258 replies (at fetch time)
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## Cited in

- 2026-07-22: [Dmitry Rybin posts a GPT-5.6 Pro counterexample to the ~30-year-old Dinitz–Garg–Goemans (Goemans cost) conjecture on unsplittable flows](https://postcutoff.com/e/2026-07-22-dinitz-garg-goemans-conjecture-disproved-gpt-5-6-pro/)