Locally sparse graph independence bound
= Locally sparse graph independence bound
There is an absolute $c>0$ such that if an $n$-vertex graph has maximum degree at most $d$ and every vertex neighbourhood spans at most $d^2/f$ edges, where $2\leq f\leq d^2$, then
$$
\alpha(G)\geq c\frac{n\log f}{d}.
$$
The triangle-free case is commonly called Shearer's independence bound.