14 problems

Let $H$ be a bipartite graph and let $G$ be a graph. Write $v(H)$ and $e(H)$ for the numbers of vertices and edges of $H$, and likewise $v(G)$ and $e(G)$ for $G$. Let $\hom(H,G)$ d…

Skokan–Thoma forcing conjecture. Every bipartite graph containing a cycle is forcing.

Let $d\ge 2$ and let $\mathcal{H}$ be a $(d-1)$-partite $(d-1)$-uniform hypergraph. For $k\in\mathbb{N}$, let $\mathcal{H}(k)$ be the $d$-partite $d$-uniform hypergraph whose $d$th…

For an $r$-uniform linear cycle $C^r_{2\ell+1}$ of odd length $2\ell+1$, let $s(C^r_{2\ell+1})$ denote its Sidorenko gap. Odd linear-cycle Sidorenko-gap conjecture. For $r\geq 3$ a…

For an $r$-partite $r$-graph $F$, let $s(F)$ be its Sidorenko gap, defined by … Assume $r\geq 3$ and … for some $0<\alpha<r-1$. The hypergraph supersaturation conjecture. There exi…

Let $F$ be a bipartite graph. Consider graphs with a prescribed number of edges, and count copies of $F$ in those graphs. Erdős–Simonovits–Sidorenko conjecture. Among all graphs wi…

Let $F$ be an $r$-uniform hypergraph and let $k$ be the uniformity of the clique $K_{k+1}^k$. Distinct edges of $F$ satisfy the $k$-linear condition when $|e\cap f|<k$ for every pa…

Let $F$ be a bipartite graph, and let $\mathrm{E}^r(F)$ denote its $r$-uniform expansion: each edge of $F$ is extended to an $r$-edge by adding new vertices. An $r$-graph is Sidore…

Saad–Wolf conjecture. Such a configuration is Sidorenko only if the coefficients $\lambda_i$ can be partitioned into zero-sum pairs. Fox, Pham, and Zhao later showed that the preci…

Directed Sidorenko conjecture. If $B$ is a bipartite oriented graph with a homomorphism $B\to\vec K_2$, then $B$ has the directed Sidorenko property. This is a directed analogue of…

Hypergraph Sidorenko conjecture. The hypergraph $X$ contains at least

Let $\mathcal{R}$ be the class of bipartite graphs admitting the reflection-complex property, and let a hypercube be the graph on ${0,1}^n$ in which two vertices are adjacent when…

Retract-smoothness conjecture. If $H$ is a Sidorenko graph and $T$ is a retract of $H$, then $T$ is smooth in $H$.

Local Sidorenko conjecture. The function $t(F,W)$ is minimized, among all nonnegative functions $W$ satisfying this constraint, by the constant function $W\equiv 1$. This is a loca…