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Sidorenko's Conjecture says that the minimum density of a bigraph $G$ in abigraphon $W$ of a given edge density is attained when $W$ is a constantfunction. A consequence of a result by B. Szegedy is that it is enough to showSidorenko's Conjecture under the further assumption that $W$ is biregular. Inthis paper, we retrieve this result with a more elementary proof. With thisbiregularity result and some ideas of its proof, we also obtain simple proofsof several other results related to Sidorenko's Conjecture. Furthermore, wealso show that bigraphs that have a special type of tree decomposition, calledreflective tree decomposition, satisfy Sidorenko's conjecture. This bothunifies and generalizes the notions of strong tree decompositions and$N$-decompositions from the literature.

Biregularity in Sidorenko's Conjecture