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…

Defective-colouring conjecture. Every $(r+1)$-uniform linear hypergraph with maximum degree at most $\Delta$ has a $d$-defective colouring with

For a graph $H$, let $\operatorname{\overline{td}}(H)$ be its connected tree-depth, and let $\mathcal{M}_H$ be the class of graphs containing no $H$ minor. Let…

For a graph class $\mathcal{G}$, let $\chi_{\Delta}(\mathcal{G})$ be the minimum integer $k$ such that, for some integer $d$, every graph in $\mathcal{G}$ is $k$-colourable with de…