  The Tur\'an number $\text{ex}(n,H)$ of a graph $H$ is the maximal number of
edges in an $H$-free graph on $n$ vertices. In $1983$ Chung and Erd\H{o}s asked
which graphs $H$ with $e$ edges minimize $\text{ex}(n,H)$. They resolved this
question asymptotically for most of the range of $e$ and asked to complete the
picture. In this paper we answer their question by resolving all remaining
cases. Our result translates directly to the setting of universality, a
well-studied notion of finding graphs which contain every graph belonging to a
certain family. In this setting we extend previous work done by Babai, Chung,
Erd\H{o}s, Graham and Spencer, and by Alon and Asodi.
