3 problems

Quasirandomness conjecture. There exists a constant-degree polynomial test that distinguishes these hypotheses with high probability if and only if one of the signed subgraph count…

Let $\mathcal{S}$ be a set of graphs. It is sparse forcing if, whenever graphs $G_n$ satisfy $|G_n|\to\infty$, have edge density $p_n=|G_n|^{-o(1)}$, and the limits … exist for eve…

For $0<p<1$, suppose there exist $\varepsilon,\eta>0$ and $n_0\in\mathbb{N}$ such that $G$ is a lower-$(p,\varepsilon)$-regular graph on $n\geq n_0$ vertices, $n$ is odd, and…