Reed's chromatic bound conjecture

Let $G$ be a graph, with maximum degree $\Delta(G)$ and clique number $\omega(G)$. Reed's conjecture. Every graph $G$ satisfies

$$\chi(G) \leq \left\lceil \frac{1}{2}(\Delta(G)+1+\omega(G))\right\rceil.$$

This refines the Borodin–Kostochka direction and is equivalent to a stronger interpolation between maximum degree and clique number. It remains open, although partial results establish related bounds with a smaller coefficient than the conjectured one.