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OP-12128Status unassessedGraph theory

Sidorenko's Conjecture (AlphaEvolve problem 26)

Sidorenko's Conjecture (AlphaEvolve problem 26). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

MSC 05C35 · Extremal problems in graph theory

Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.

Licensed source statementAs of Repository at commit 8f44745 (2026-07-11); the repository records AlphaEvolve results, not current research statusSource & evidence ↓
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Problem statement

A graphon is a symmetric measurable function W ⁣:[0,1]2→[0,1]W \colon [0,1]^2 \to [0,1]. Given a graphon WW and a finite graph H=(V(H),E(H))H = (V(H),E(H)), the homomorphism density t(H,W)t(H,W) is defined as

t(H,W)=∫[0,1]V(H)∏{v,w}∈E(H)W(xv,xw)∏v∈V(H)dxv.t(H,W) = \int_{[0,1]^{V(H)}} \prod_{\{v,w\} \in E(H)} W(x_v,x_w) \prod_{v \in V(H)} dx_v.

For a finite bipartite graph HH, let C(H)C(H) denote the least constant for which

t(H,W)≥t(K2,W)C(H)t(H, W) \geq t(K_2, W)^{C(H)}

holds for all graphons WW, where K2K_2 is the complete graph on two vertices. What is C(H)C(H)?

Lean 4

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Background

The repository status chart does not categorize this problem. See Section 6.11, in "Mathematical Exploration and Discovery at Scale " paper: arXiv:2511.02864. Experiment notebook.

Progress & source assessment

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References
  1. [1]Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Repository of problems accompanying “Mathematical exploration and discovery at scale” (arXiv:2511.02864), github.com/google-deepmind/alphaevolve_repository_of_problems (commit 8f44745, 11 July 2026). — Sidorenko's Conjecture (AlphaEvolve problem 26) linkApache-2.0 (repository license); problem pages reproduced with attribution.

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