7 problems

Let $s,t$ be integers with $t\geqslant s\geqslant 1$, and let $\mathcal{B}_{s,t}$ be the class of graphs containing no $K_{s,t}$ minor. For a fixed graph $H$, define an $s$-separat…

A graph class $\mathcal{G}$ is nice if it is minor-closed and does not contain $K_{3,t}$ for some positive integer $t$. Havet–van den Heuvel–McDiarmid–Reed conjecture. There exists…

Let $\mathcal{F}$ be a minor- and union-closed family of graphs, and let $\cong_{\mathcal{F}}$ denote homomorphism indistinguishability over $\mathcal{F}$. Non-isomorphism conjectu…

Let $\mathcal{F}$ be a family of graphs. Call it homomorphism distinguishing closed if, for every graph $F\notin\mathcal{F}$, there exist graphs $G$ and $H$ such that…

Let $\mathcal{F}_1$ and $\mathcal{F}_2$ be minor- and union-closed families of graphs. Write $\cong_{\mathcal{F}_1}\Rightarrow\cong_{\mathcal{F}_2}$ when the first homomorphism ind…

Let $\mathcal{F}_1$ and $\mathcal{F}_2$ be two distinct minor- and union-closed families of graphs. For a graph family $\mathcal{F}$, write $G\cong_{\mathcal{F}}H$ when $G$ and $H$…

List-colouring extension of Wegner's conjecture.