7 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…

Gerards–Seymour odd Hadwiger conjecture. For all $t\geq 2$, every graph with no odd $K_t$ minor is $(t-1)$-colorable.

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 $f_o(t)$ be the smallest integer such that every graph with no odd-$K_t$ minor is $f_o(t)$-colorable, where an odd-$K_t$ minor is defined using a 2-coloring of vertices and $t$…

Odd Hadwiger's conjecture. For every integer $t \geq 1$, every graph with no odd $K_t$ minor is $(t-1)$-colorable.

The odd Hadwiger conjecture. Every graph with no odd $K_t$ minor is $(t-1)$-colorable.