ChatGPT proves Dinitz-Garg-Goemans conjecture is false

A user claims to have disproven the Dinitz-Garg-Goemans conjecture, a graph theory problem open for ~30 years, using ChatGPT 5.6 Pro. The user states the graph below has fractional flow cost 58, while any unsplittable flow with capacity violation ≤15 has cost at least 60, providing a counterexample.

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: - 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. - The conjecture was based on absolutely stunning result of Dinitz, Garg, and Goemans: any fractional flow can be routed to unsplittable flow by violating graph capacities by at most max demand . The chat with gpt pro here is an absolute meme - Your 'many weeks thinking about it' was asking the model to try again 4x. 😂 Join the conversation