{"paper":{"title":"Characterizing Polytopes Contained in the $0/1$-Cube with Bounded Chv\\'atal-Gomory Rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM"],"primary_cat":"math.OC","authors_text":"Samuel Fiorini, Stefan Weltge, Tony Huynh, Yohann Benchetrit","submitted_at":"2016-11-20T21:10:07Z","abstract_excerpt":"Let $S \\subseteq \\{0,1\\}^n$ and $R$ be any polytope contained in $[0,1]^n$ with $R \\cap \\{0,1\\}^n = S$. We prove that $R$ has bounded Chv\\'atal-Gomory rank (CG-rank) provided that $S$ has bounded notch and bounded gap, where the notch is the minimum integer $p$ such that all $p$-dimensional faces of the $0/1$-cube have a nonempty intersection with $S$, and the gap is a measure of the size of the facet coefficients of $\\mathsf{conv}(S)$.\n  Let $H[\\bar{S}]$ denote the subgraph of the $n$-cube induced by the vertices not in $S$. We prove that if $H[\\bar{S}]$ does not contain a subdivision of a la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06593","kind":"arxiv","version":3},"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"}