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The integrality gap of this relaxation is known as the Grothendieck constant $\\ka(G)$ of $G$. We present a closed-form formula for the Grothendieck constant of $K_5$-minor free graphs and derive that it is at most 3/2. Moreover, we show that $\\ka(G)\\le \\ka(K_k)$ if the cut polytope of $G$ is defined by inequaliti"},"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":"1106.2735","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-10T21:34:45Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"63e1a1cbea0d9fb51d2a0ad2e81545ecfcf878b7273bfabd8d16bec9686cd558","abstract_canon_sha256":"ba8a9a7913390d2b3ba7b98d0b2f69a450162e0a8b93e12a61bec27310a461a1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:04.232031Z","signature_b64":"pkZeDUaJNbWuLXEjUKh5XC0bBBGswZkW+sgBHSN7RoMhgXFOwBH3XoXzoBBOf2hYRdKkZUuwzUz8JJTqgj5yCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b047b31c93552e9589188db3e4c037dddb8e8bfdc365bcf9176759bd359c41b5","last_reissued_at":"2026-05-18T04:20:04.231625Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:04.231625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing the Grothendieck constant of some graph classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Antonios Varvitsiotis, Monique Laurent","submitted_at":"2011-06-10T21:34:45Z","abstract_excerpt":"Given a graph $G=([n],E)$ and $w\\in\\R^E$, consider the integer program ${\\max}_{x\\in \\{\\pm 1\\}^n} \\sum_{ij \\in E} w_{ij}x_ix_j$ and its canonical semidefinite programming relaxation ${\\max} \\sum_{ij \\in E} w_{ij}v_i^Tv_j$, where the maximum is taken over all unit vectors $v_i\\in\\R^n$. The integrality gap of this relaxation is known as the Grothendieck constant $\\ka(G)$ of $G$. We present a closed-form formula for the Grothendieck constant of $K_5$-minor free graphs and derive that it is at most 3/2. 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