AlphaEvolve problems·alphaevolve:26
Sidorenko's Conjecture
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A graphon is a symmetric measurable function $W \\colon [0,1]^2 \\to [0,1]$. Given a graphon $W$ and a finite graph $H = (V(H),E(H))$, the homomorphism density $t(H,W)$ is defined as $$ t(H,W) = \\int_{[0,1]^{V(H)}} \\prod_{\\{v,w\\} \\in E(H)} W(x_v,x_w)\ \\prod_{v \\in V(H)} dx_v.$$ For a finite bipartite graph $H$, let $C(H)$ denote the least constant for which $$t(H, W) \\geq t(K_2, W)^{C(H)}$$ holds for all graphons $W$, where $K_2$ is the complete graph on two vertices. What is $C(H)$?
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qed.bot, “Sidorenko's Conjecture”, https://qed.bot/t/alphaevolve-26, as of 30 Sep 2026.