{"id":"openai-math/A-counterexample-to-Sidorenkos-conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/A-counterexample-to-Sidorenkos-conjecture-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-counterexample-to-Sidorenkos-conjecture-September-23-2026","tags":["graph-homomorphisms","extremal-combinatorics","graph-densities","quasirandomness"],"score":0,"title":"A counterexample to Sidorenko's conjecture","domain":"Combinatorics","family":"161","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"We disprove Sidorenko's conjecture with a bipartite graph on 35 vertices and 66 edges: its homomorphism density in some finite simple graph is smaller than the conjectured lower bound. The same connected graph also disproves the forcing conjecture: at one fixed density, asymptotically matching the edge and pattern densities does not imply quasirandomness.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-23","reactions":{},"discussion":[{"url":"https://gilkalai.wordpress.com/2026/10/07/updates-sharing-ai-progress-on-mathematics-amazing-and-my-lecture-plans/#:~:text=has%2035%20vertices%20and%2066%20edges%20and%20also%20disproves%20the%20related%20forcing%20conjecture","date":"2026-10-07","kind":"web","site":"Combinatorics and more","text":"has 35 vertices and 66 edges and also disproves the related forcing conjecture. Ryser’s covering conjecture. I discussed Ryser’s conjecture in my birthday post for Ron Aharoni, including his proof of the tripartite case. The new counterexamples are intersecting -partite, -uniform hypergraphs…","added":"2026-10-24","title":"Updates: Sharing AI progress on mathematics (amazing!); and my lecture plans"}],"formalized":false,"family_title":"Counterexamples to Sidorenko’s conjecture and the forcing conjecture"}