{"paper":{"title":"0/1 Polytopes with Quadratic Chvatal Rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.DM"],"primary_cat":"math.CO","authors_text":"Laura Sanita, Thomas Rothvoss","submitted_at":"2012-04-20T22:01:17Z","abstract_excerpt":"For a polytope P, the Chvatal closure P' is obtained by simultaneously strengthening all feasible inequalities cx <= b (with integral c) to cx <= floor(b). The number of iterations of this procedure that are needed until the integral hull of P is reached is called the Chvatal rank. If P is a subset of [0,1]^n, then it is known that O(n^2 log n) iterations always suffice (Eisenbrand and Schulz (1999)) and at least (1+1/e-o(1))n iterations are sometimes needed (Pokutta and Stauffer (2011)), leaving a huge gap between lower and upper bounds.\n  We prove that there is a polytope contained in the 0/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4753","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}