the grothendieck-knudsen moduli space $\bar m_{0,n}$ of stable, $n$-pointed rational curves has a natural stratification given by topological type. it is a natural question whether the boundary generates the effective cone of divisors, or whether the one-dimensional strata generate the effective cone of curves (the fulton conjecture). we construct many (non-boundary) divisors that are generators of the effective cone, as well as rigid curves intersecting the interior. the main technique is to identify $m_{0,n}$ with the brill-noether locus of a reducible curve given by a hypergraph. this is joint work with jenia tevelev.