5 problems

The above-threshold product-structure conjecture. For every $\alpha \geq s(n)$, the class of intersection graphs of $\alpha$-free homothetic regular $n$-gons has product structure.

Product-structure conjecture for $k$-independent crossing graphs. The class of $k$-independent crossing graphs admits product structure.

The no-product-structure conjecture. For every $\alpha < s(n)$, the class of intersection graphs of $\alpha$-free homothetic regular $n$-gons does not have product structure.

The canonical-drawing characterization. The class of intersection graphs of $\alpha$-free homothetic regular $n$-gons admits product structure if and only if their canonical drawin…

Polynomial-growth product-structure conjecture. There exist functions $g\colon\mathbb{R}\times\mathbb{N}\to\mathbb{N}$ and $h\colon\mathbb{R}\times\mathbb{N}\to\mathbb{R}$ such tha…