An edge-weighted graph (V, E) is a cut-model for an edge-weighted hypergraph (V, H) if the weight of the edges cut by any bipartition of V in the graph is the same as the weight of the hyperedges cut by the same bipartition in the hypergraph. We show that there is no cut-model in general.

Next we examine whether the addition of dummy vertices helps: An edge-weighted graph (V D, E) is a mincut-model for an edge-weighted hypergraph (V, H) if the weight of the hyperedges cut by a bipartition of the hypergraphs vertices is the same as the weight of a minimum cut separating the two parts in the graph. We construct such models using positive and negative weights. On the other hand, we show that there is no mincut-model in general if only positive weights are allowed.