A note on directed analogues of the Sidorenko and forcing conjectures

TL;DR

This paper explores directed versions of the Sidorenko and forcing conjectures, demonstrating their equivalence to the undirected versions, thus linking directed and undirected graph conjectures.

Contribution

It establishes the equivalence between natural directed graph variants of the conjectures and their undirected counterparts, providing new insights into their relationships.

Findings

Directed variants are equivalent to undirected analogues

Provides a unified perspective on Sidorenko and forcing conjectures

Bridges the gap between directed and undirected graph conjectures

Abstract

We study analogues of Sidorenko's conjecture and the forcing conjecture in oriented graphs, showing that natural variants of these conjectures in directed graphs are equivalent to the asymmetric, undirected analogues of the conjectures.