Conflict hypergraphs to define new families of facets for the independence system polytope

In this paper, we develop a technique for exact simultane- ous upliftings of circuit inequalities of an independence system poly- tope. The resulting inequalities define new families of valid inequal- ities for this polytope. They are obtained by simultaneously adding the most appropriate set of variables with the highest possible values of the lifting coefficient that maintain the validity. More specifically, in this technique, we introduce a procedure to generate two conflict hypergraph structures types: hypertrees and clutter. In this setting, we use the hyperedges cardinalities of these structures to compute the suitable lifting coefficient values. We then give necessary and sufficient conditions for both the circuit inequalities and the new families of valid inequalities to be facet-defining.