Convex graphon parameters and graph norms

Sidorenko’s conjecture states that the number of copies a bipartite graph H in G is asymptotically minimised when quasirandom graph. A notorious example where this remains open = K5,5C10. It was even unknown whether possesses strictly stronger, weakly norming property.We take step towards understanding K5,5C10 by proving it not norming. More generally, we show ‘twisted’ blow-ups cycles, which include and C6?K2, are This answers two questions Hatami. The method relies on analysis Hessian matrices defined homomorphisms, using equivalence between (weakly) property convexity homomorphism densities. We also prove Kt,t minus perfect matching, proven to be Lovász, for every t > 3.