Abstract The famous Sidorenko’s conjecture asserts that for every bipartite graph H, the number of homomorphisms from H to a graph G with given edge density is minimised when G is pseudorandom. We prove that for any graph H, a graph obtained from replacing edges of H by generalised theta graphs consisting of even paths satisfies Sidorenko’s conjecture, provided a certain divisibility condition on the number of paths. To achieve this, we prove unconditionally that bipartite graphs obtained from replacing each edge of a complete graph with a generalised theta graph satisfy Sidorenko’s conjecture, which extends a result of Conlon, Kim, Lee and Lee J. Lond. Math. Soc. , 2018.
Im et al. (Wed,) studied this question.