Bipartite Graphs - Maximum subset of one partition with at most n neighbours - NP-hard?
It's NP-complete by a reduction from cliques in graphs. Given an arbitrary graph $G$, construct a bipartite graph from its incidence matrix, by making one side $U$ of the bipartition correspond to the edges of $G$ and the other side correspond to the vertices of $G$. Then $G$ has a clique of size $\omega$ if and only if the constructed bipartite graph has a set of $\binom{\omega}{2}$ vertices in $U$ that has at most $\omega$ neighbors on the other side of the bipartition.