4 problems

Let $H$ be a graph, let $\mathcal{G}_H^{\text{odd}}$ be the class of graphs with no $H$ odd-minor, let $\operatorname{\overline{td}}(H)$ denote the connected tree-depth of $H$, let…

Let $\mathcal{X}_{k,c}$ be the graph family defined in the source, and let $\mathcal{M}$ be a minor-closed class. NSSW excluded-configuration conjecture. Every minor-closed class t…

Let $\mathcal{V}_k:=\{G:\mu(G)\leqslant k\}$, where $\mu(G)$ is the Colin de Verdière parameter, and let $\chi_{\star}(\mathcal{V}_k)$ be the clustered chromatic number of this cla…

Let $\mathcal{M}$ be a minor-closed class of graphs, and let $k\geqslant 0$ be an integer. A graph class is $k$-cluster critical if it is obtained as a wedge-product of $v$ copies…