9 problems

Let $F$ be a bipartite graph, and suppose that its ordinary Turán number satisfies … At the threshold $p=1/(1-\alpha)$, the logarithmic factor in the corresponding critical-point u…

Let $r\ge 2$ be an integer, and let $\mathcal{F}$ be a degenerate family of $r$-graphs satisfying $ex{ex}(n,\mathcal{F})=O(n^{1+\alpha})$ for some constant $\alpha\ge r-2$. Set … T…

Let $H$ be a bipartite graph, let $t_H(f)$ be its homomorphism density functional, and let a stable involution of $H$ mean the graph-theoretic object specified by the source. Posit…

Let $H$ be a bipartite graph, let $t_H(f)$ denote its homomorphism density functional, and let the stable involution group be the corresponding group of stable involutions of $H$.…

Let $H$ be a bipartite graph. Its cut involution group is the group of graph symmetries generated by cut involutions, and $H$ is weakly norming when its associated homomorphism-den…

Schatten norm conjecture for r-partite graphs. If $G$ is an $r$-partite graph of order $n$, then

Strict Schatten norm conjecture. If $p>2$ and $G$ is a graph of order $n$, then

Sharp Schatten norm conjecture. If $p>2$ and $G$ is a graph of size $m$, then

Strict upper-bound conjecture. There exist infinitely many positive integers $k$ such that