7 problems

Graphon quasirandomness conjecture. If there exists a constant-degree polynomial test distinguishing $\mathbb{G}(n,1/2)$ from any graphon, then the two distributions can also be di…

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…

Glock–Kühn–Osthus conjecture. The same result should hold for such graphs $G$ with odd order.

Let $H$ be a graph, and let $\{K_2,H\}$ be the family consisting of the single edge $K_2$ and $H$. A graph family is forcing if, for every $0<p<1$, every sufficiently large $n$-ver…

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…

Let $H$ be a bipartite graph with at least one cycle. In the dense setting, where the edge density $p_n$ is constant, a set of graphs is forcing if convergence of the relevant norm…

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…