5 problems

A graphon $W$ is $\rho$-locally dense if … for every measurable set $S\subseteq[0,1]$. A finite graph $H$ is called KNRS if every $\rho$-locally dense graphon satisfies…

The positive graph conjecture. A graph $H$ is positive if and only if it has a stable involution.

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…

Let $H$ be an $r$-uniform hypergraph, or $r$-graph. Call $H$ positive when its corresponding hypergraph homomorphism-density functional is nonnegative for every bounded measurable…

Let $G$ be a graph. Its homomorphism density is … for every bounded measurable symmetric function $f:[0,1]^2\to\mathbb{R}$, and $G$ is positive when $t_G(f)\geq 0$ for all such $f$…