3 problems

Odd chromatic number conjecture. If $G$ is a connected graph of maximum degree $\Delta\geq3$, then

Let $G$ be a finite simple graph, let $\operatorname{mad}(G)$ be the maximum of $\frac{2|E(H)|}{|V(H)|}$ over all non-empty subgraphs $H$ of $G$, and let $\chi_o(G)$ be the least p…

Let $G$ be a connected graph with maximum degree $\Delta$. Maximum-degree odd chromatic number conjecture. If $\Delta\geq3$, then … This would extend the preceding bounds for subcu…