A counterexample to Sidorenko's conjecture
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OpenAI
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.
Claims
SOLUTION CLAIMED
OP-00715 — Sidorenko's lower bound for bipartite homomorphism counts
Files and sources
- Paper
- math @ 1581d4c, build/main.tex ↗
- Posted on GitHub
- 6 October 2026
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