7 problems

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

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