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A famous conjecture of Sidorenko and Erd\H{o}s-Simonovits states that if H isa bipartite graph then the random graph with edge density p has in expectationasymptotically the minimum number of copies of H over all graphs of the sameorder and edge density. The goal of this expository note is to give a shortself-contained proof (suitable for teaching in class) of the conjecture if Hhas a vertex complete to all vertices in the other part.

Sidorenko's conjecture for a class of graphs: an exposition