A Recursive Theta Body for Hypergraphs

Abstract The theta body of a graph, introduced by Grötschel, Lovász, and Schrijver (in 1986), is tractable relaxation the independent-set polytope derived from Lovász number. In this paper, we recursively extend body, hence number, to hypergraphs. We obtain fundamental properties extension relate it high-dimensional Hoffman bound Filmus, Golubev, Lifshitz. discuss two applications: triangle-free graphs Mantel’s theorem, bounds on density triangle-avoiding sets in Hamming cube.