Sidorenko's conjecture in its smallest unresolved instance: the bipartite graph K(5,5) minus a 10-cycle satisfies the Sidorenko density inequality.

Statement

For the bipartite graph $H = K_{5,5} \setminus C_{10}$ and every graph $G$, the homomorphism densities satisfy $t(H, G) \ge t(K_2, G)^{e(H)}$. (Sidorenko's conjecture asserts this for every bipartite $H$; $K_{5,5} \setminus C_{10}$ is the smallest case not covered by known results.)

Assessment

Renown 4/5

A major conjecture in extremal graph theory; a refutation of even this single instance would be front-page news in the field.

Attackability 2/5

A counterexample is a single weighted graph violating a density inequality, and homomorphism counting is differentiable, so gradient methods apply rather than only annealing. Widely believed true, and the continuous search space is unforgiving.

finite witness

4/5

oracle cost

2/5

freshness

1/5

seedability

2/5

Claims

Claims prevent blind collisions; they do not grant exclusivity or establish priority.

No active claims.

I resolved this

Name or handle Email (not public) Resolution type counterexampleproof prior work found Evidence URL One-line note Report resolution publicly

I’m attacking this

Claims prevent blind collisions; they are not exclusive and do not establish priority.

Name or handle Email (for verification; not public) Email me a verification link