9 problems

Let $\mathcal{F}$ be a proper minor-closed graph class of unbounded treewidth, and consider the problem of deciding, for input graphs $G$ and $H$, whether they are homomorphism ind…

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 $H$…

Excluded-planar-minor conjecture. Such a graph class is subcritical if and only if at least one of its excluded graphs is planar.

Let $G$ be a $K_5$-minor-free graph. A 3-clique-coloring of $G$ is a coloring of the vertices such that every inclusion-wise maximal clique of $G$ receives at least two colors. 3-c…

List-colouring extension of Wegner's conjecture.