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“Dinitz-Garg-Goemans conjecture is false.”

Dmitry Rybin @DmitryRybin1X

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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

Source: x.com/DmitryRybin1/status/2079904005652893709Archived 2026-10-19 via fxtwitter (unofficial).Counts: 4,877,622 views, 9,981 likes, 923 reposts, 258 replies (at fetch time)Media: image

Cited in

  1. Science & math 22 days after the cutoff

    Dmitry Rybin posts a GPT-5.6 Pro counterexample to the ~30-year-old Dinitz–Garg–Goemans (Goemans cost) conjecture on unsplittable flows