6 problems

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

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 $G$,

Let $G_1$ and $G_2$ be graphs on a common vertex set of size $n$, with $G_1\cup G_2=K_n$, and let $\ngsl{\beta}(2;n)$ denote the minimum of $\beta(G_1)+\beta(G_2)$ over such decomp…