Abstract: More than 1000 years ago, Alcuin proposed a classical puzzle involving a wolf, a goat and a bunch of cabbages. Recently, Prisner and Csorba et al. considered this transportation planning problem that generalizes Alcuin's river crossing problem to arbitrary conflict graphs $G$. In this paper we generalize this problem to arbitrary hypergraphs $H=(V,\mathcal{E})$. Now the man has to transport a set $V$ of items/vertices across the river. Some items of $V$ formed  a hyperedge in $\mathcal{E}$ iff they are conflicting and thus cannot be left together without human supervision. The Alcuin number of a conflict hypergraph is the smallest capacity of a boat for which the hypergraph possesses a feasible schedule. In this paper we give the Alcuin numbers of complete bipartite $r$-uniform hypergraphs and their adjoint hypergraphs, $r$-uniform hypergraphs. We also prove that it's NP-hard to decide whether a given $r$-uniform hypergraph is a small boat hypergraph.

Key words: Alcuin number, transversal set, independent set