6 problems

Pang–Miao–Fan's conjecture. Every planar graph admits a strong odd $13$-coloring; equivalently,

For a graph $G$, define its maximum average degree by … An odd $c$-coloring is a proper coloring with $c$ colors in which every non-isolated vertex has a color appearing an odd num…

Let $G$ be a graph, let $mad(G)$ denote its maximum average degree, let $\chi_o(G)$ denote its odd chromatic number, and let $c$ be an integer with $c\ge 4$. Cho's conjecture. If ……

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…