Sidorenko's conjecture
Sidorenko's conjecture is a major conjecture in the field of extremal graph theory, posed by Alexander Sidorenko in 1986. Roughly speaking, the conjecture states that for any bipartite graph H {\displaystyle H} and graph G {\displaystyle G} on n {\displaystyle n} vertices with average degree p n {\displaystyle pn} , there are at least p | E ( H ) | n | V ( H ) | {\displaystyle p^{|E(H)|}n^{|V(H)|}} labeled copies of H {\displaystyle H} in G {\displaystyle G} , up to a small error term.