False Graph Theory Conjecture

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: Flow Cost Demand s w u v t1 t2 t3 d = 15 d = 10 3 6 10 2 24 4 5 9 14 5 10 2

A screenshot of an X post claims that the Dinitz–Garg–Goemans conjecture is false after a graph theory problem remained open for about 30 years. It shows a directed network diagram and says the graph has fractional flow cost 58, while any unsplittable flow with capacity violation at most 15 costs at least 60. The joke is an absurdly confident mathematical breakthrough attributed to a chat with GPT, making it a reaction to AI-generated or questionable proof claims.

• @gentoomemes / 21430 2026-07-22