Left-cut-percolation and induced-Sidorenko bigraphs

Understand

A Sidorenko bigraph is one whose density in a bigraphon $W$ is minimized precisely when $W$ is constant.

• Several techniques of the literature to prove the Sidorenko property consist of decomposing (typically in a tree decomposition) the bigraph into smaller building blocks with stronger properties.
• One prominent such technique is that of $N$-decompositions of Conlon--Lee, which uses weakly H\"{o}lder (or weakly norming) bigraphs as building blocks.
• In turn, to obtain weakly H\"{o}lder bigraphs, it is typical to use the chain of implications reflection bigraph $\implies$ cut-percolating bigraph $\implies$ weakly H\"{o}lder bigraph.