5 problems

Independence-number lower-bound conjecture. For any graph $G$,

Chromatic lower-bound conjecture. For any graph $G$,

Strong $\delta$-conjecture for $\nu$. For any graph $G$,

Weak Graph Complement Conjectures. There exist universal constants $b,b_+,b_\nu<2$ such that, for every graph $G$,

Graph Complement Conjecture for $\nu$. For any graph $G$,