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We consider the multilinear polytope defined as the convex hull of the set ofbinary points satisfying a collection of multilinear equations. The complexityof the facial structure of the multilinear polytope is closely related to theacyclicity degree of the underlying hypergraph. We obtain a polynomial-sizeextended formulation for the multilinear polytope of beta-acyclic hypergraphs,hence characterizing the acyclic hypergraphs for which such a formulation canbe constructed.

A polynomial-size extended formulation for the multilinear polytope of beta-acyclic hypergraphs