Partitioning of Hypergraphs

Let H = (V, E) be an undirected hypergraph and Asubset of or equal toC. We consider the problem of finding a minimum cost partition of V that separates every pair of nodes in A. We consider three formulations of the problem and show that the theoretical lower bounds to the integer optimal objective value provided by the LP-relaxations in all three cases are identical. We describe our empiical findings with each formulation.