An elegant and general way to apply graph partitioning algorithms to hypergraphs would be to model hypergraphs by graphs and apply the graph algorithms to these models. Of course such m o d e l s h a ve t o s i m ulate the given hypergraphs with respect to their cut properties. An edge-weighted graph (V E) i s a cut-model for an edge-weighted hypergraph (V H) if the weight of the edges cut by a n y bipartition of V in the graph is the same as the weight of the hyperedges cut by the same bipartition in the hypergraph. We s h o w that there is no cut-model in general. Next we examine whether the addition of dummy v ertices helps: An edge-weighted graph (V D E) i s a mincut-model for an edge-weighted hypergraph (V H) i f t h e 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 w eights. On the other hand, we s h o w t h a t there is no mincut-model in general if only positive w eights are allowed.
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