Erdős's girth conjecture

Let $l,n$ be positive integers. A graph with girth $2l+1$ and $n$ vertices is said to have many edges if its number of edges is bounded below by a positive constant times $n^{1+\frac{1}{l}}$. Erdős's conjecture. For any positive integers $l,n$, there exists a graph with girth $2l+1$, $n$ vertices and $\Omega(n^{1+\frac{1}{l}})$ edges. This conjecture concerns the extremal number of edges in graphs of prescribed odd girth and is related to the sharpness of upper bounds for graph radius in terms of minimum degree and girth.