3 problems

Let $H$ and $G$ be graphs, let $t(H,G)$ denote the homomorphism density of $H$ in $G$, and call an $n$-vertex graph $G$ $(\rho,d)$-nearly-regular when all but at most $\rho n$ vert…

Let $H$ and $G$ be graphs, let $t(H,G)$ denote the homomorphism density of $H$ in $G$, and call an $n$-vertex graph $G$ $(\rho,d)$-dense when every subset $X$ of at least $\rho n$…

The doubly nonnegative function and good graph conjecture. All doubly nonnegative functions are nice, and all simple graphs are good.