Facets of the independent set polytope

Theoretical results pertaining to the independent set polytope P-ISP=conv{xis an element of{0,1}(n):Axless than or equal tob} are presented. A conflict hypergraph is constructed based on the set of dependent sets which facilitates the examination of the facial structure of P-ISP. Necessary and sufficient conditions are provided for every nontrivial 0-1 facet-defining inequalities of P-ISP in terms of hypercliques. The relationship of hypercliques and some classes of knapsack facet-defining inequalities are briefly discussed. The notion of lifting is extended to the conflict hypergraph setting to obtain strong valid inequalities, and back-lifting is introduced to strengthen cut coefficients. Preliminary computational results are presented to illustrate the usefulness of the theoretical findings.