5 problems

Linear Ramsey–co-chromatic conjecture. A finitely defined hereditary class is of linear Ramsey numbers if and only if it has bounded co-chromatic number.

Let $G$ be sampled from the binomial random graph model $G_{n,1/2}$, and let $u$ denote the chromatic number of $G$ and $barchi$ its cochromatic number, so that the gap is…

Let $G$ be sampled from the binomial random graph $G_{n,1/2}$, and let $\chi(G)$ and $\zeta(G)$ denote its chromatic and cochromatic numbers, respectively. Here, “with high probabi…

Let $G$ be a graph, and write $\omega(G)$ for its clique number, $\zeta(G)$ for its cochromatic number, and $\chi(G)$ for its chromatic number. Erdős, Gimbel and Straight's conject…

For a surface $S_g$ of orientable genus $g$, let $Z(S_g)$ denote the maximum fractional? cocoloring? [Context defines $Z(S_g)$ as the surface maximum of the cochromatic number.] St…