GPT 5.6 Pro finds counterexample to Dinitz-Garg-Goemans conjecture

GPT 5.6 Pro has found a counterexample to the Dinitz-Garg-Goemans conjecture, a graph theory problem open for approximately 30 years. The graph exhibits a fractional flow cost of 58, while any unsplittable flow with capacity violation ≤15 has cost at least 60, disproving the conjecture. The user who discovered the counterexample stated they spent many weeks thinking about the problem.

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: chatgpt.com/share/6a60b2eb-0… https://chatgpt.com/share/6a60b2eb-0b64-83ee-9c76-7931ca1de063 Jul 22, 2026 · 12:18 PM UTC 186 662 7,566 2,566,273 I know counterexamples to old conjectures are becoming a meme at this point. But I really cared about this problem and spent many weeks thinking about it a while ago in both directions, proof and disproof . I think almost all graph flows experts thought about this problem. 12 11 1,536 107,200