5 problems

Let $r,s\ge 3$, and for graphs $H_1,H_2$ let $\delta_\chi(H_1,H_2)$ denote the minimum-degree density above which every graph admitting a red-blue edge-coloring with no red copy of…

Thundercloud-forest conjecture. The chromatic threshold satisfies

Łuczak–Thomassé conjecture. The family $\mathcal{B}$ has chromatic threshold

Boundedness-at-threshold conjecture. For every graph $H$ with $\delta_\chi(H)=\lambda(H)$, there exists a constant $C(H)$ such that

Łuczak–Thomassé conjecture. The chromatic threshold of $H$ satisfies