A recursive theta body for hypergraphs
Abstract
The theta body of a graph, introduced by Grötschel, Lovász, and Schrijver in 1986, is a tractable relaxation of the independentset polytope derived from the Lovász theta number. In this paper, we recursively extend the theta body, and hence the theta number, to hypergraphs. We obtain fundamental properties of this extension and relate it to the highdimensional Hoffman bound of Filmus, Golubev, and Lifshitz. We discuss two applications: trianglefree graphs and Mantel's theorem, and bounds on the density of triangleavoiding sets in the Hamming cube.
 Publication:

arXiv eprints
 Pub Date:
 June 2022
 DOI:
 10.48550/arXiv.2206.03929
 arXiv:
 arXiv:2206.03929
 Bibcode:
 2022arXiv220603929C
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Optimization and Control;
 05C15;
 68R10;
 90C27
 EPrint:
 23 pages, 2 figures