3 problems

Odd-minor Duchet–Meyniel conjecture. For any graph $G$ of order $n$,

Let $G$ be a finite simple graph with independence number $\alpha(G)$ and chromatic number $\chi(G)$. For positive integers $\ell$ with $2\ell\leq\chi(G)$, let…

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…