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Let $\\mathsf{STAB}(G)$ be the convex hull of the stable sets of $G$. It is easy to see that $n \\leqslant \\mathsf{xc} (\\mathsf{STAB}(G)) \\leqslant n+m$. We improve both of these bounds. For the upper bound, we show that $\\mathsf{xc} (\\mathsf{STAB}(G))$ is $O(\\frac{n^2}{\\log n})$, which is an improvement when $G$ has quadratically many edges. For the lower bound, we prove that "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.08741","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-02-28T11:03:47Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"bf1ce3ca8b119a9adb1b1dea7f1a2363d23e66ee146d7d5496ccf473fa5e9ec0","abstract_canon_sha256":"99cc11146f72a76e91459aaba89624e10608bec35835bd208c03a7ff3c4ea03a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:08.605984Z","signature_b64":"4/Q3HvQ7Z5DSCOXdNhcaPgFxti1mj0gs5+gMOdNYvD4j1b3heWINc57Y8vXgiUn9yZuXemjsxPQh7k8/5TwvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b89340524c6ba4618a065bf70173e3ae9b330d544690aca63c1e130feeb66b3","last_reissued_at":"2026-05-18T00:43:08.605287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:08.605287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extension complexity of stable set polytopes of bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Manuel Aprile, Marco Macchia, Samuel Fiorini, Tony Huynh, Yuri Faenza","submitted_at":"2017-02-28T11:03:47Z","abstract_excerpt":"The extension complexity $\\mathsf{xc}(P)$ of a polytope $P$ is the minimum number of facets of a polytope that affinely projects to $P$. Let $G$ be a bipartite graph with $n$ vertices, $m$ edges, and no isolated vertices. Let $\\mathsf{STAB}(G)$ be the convex hull of the stable sets of $G$. It is easy to see that $n \\leqslant \\mathsf{xc} (\\mathsf{STAB}(G)) \\leqslant n+m$. We improve both of these bounds. For the upper bound, we show that $\\mathsf{xc} (\\mathsf{STAB}(G))$ is $O(\\frac{n^2}{\\log n})$, which is an improvement when $G$ has quadratically many edges. 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