{"paper":{"title":"Semidefinite programming bounds on fractional cut-cover and maximum 2-SAT for highly regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Semidefinite programming bounds the fractional cut-cover of graphs in association schemes by their smallest eigenvalue.","cross_cats":["math.CO"],"primary_cat":"math.OC","authors_text":"Gabriel Coutinho, Henrique Assump\\c{c}\\~ao","submitted_at":"2025-05-15T17:56:11Z","abstract_excerpt":"We use semidefinite programming to bound the fractional cut-cover parameter of graphs in association schemes in terms of their smallest eigenvalue. We also extend the equality cases of a primal-dual inequality involving the Goemans-Williamson semidefinite program, which approximates MAXCUT, to graphs in certain coherent configurations. Moreover, we obtain spectral bounds for MAX 2-SAT when the underlying graphs belong to a symmetric association scheme by means of a certain semidefinite program used to approximate quadratic programs, and we further develop this technique in order to explicitly "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We use semidefinite programming to bound the fractional cut-cover parameter of graphs in association schemes in terms of their smallest eigenvalue.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The graphs under consideration belong to an association scheme or coherent configuration, which supplies the algebraic structure needed to formulate the SDP and relate it to the smallest eigenvalue.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"SDP techniques bound fractional cut-cover and MAX 2-SAT on association scheme graphs and distance-regular graphs, extending Goemans-Williamson equality cases and computing gauge duals.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Semidefinite programming bounds the fractional cut-cover of graphs in association schemes by their smallest eigenvalue.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"606360674bd238719e4f3e8a7ddbe6dd9017a0c7e6eb2f461ddd1f20e8ab8d9d"},"source":{"id":"2505.10548","kind":"arxiv","version":4},"verdict":{"id":"7f088869-a312-489d-a936-fb0fb269c2fb","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-22T14:23:11.754873Z","strongest_claim":"We use semidefinite programming to bound the fractional cut-cover parameter of graphs in association schemes in terms of their smallest eigenvalue.","one_line_summary":"SDP techniques bound fractional cut-cover and MAX 2-SAT on association scheme graphs and distance-regular graphs, extending Goemans-Williamson equality cases and computing gauge duals.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The graphs under consideration belong to an association scheme or coherent configuration, which supplies the algebraic structure needed to formulate the SDP and relate it to the smallest eigenvalue.","pith_extraction_headline":"Semidefinite programming bounds the fractional cut-cover of graphs in association schemes by their smallest eigenvalue."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.10548/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":32,"sample":[{"doi":"","year":2007,"title":"P. Austrin. Balanced max 2-sat might not be the hardest. InProceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing, STOC ’07, page 189–197, New York, NY, USA, 2007. Association for","work_id":"c4ab773d-b67a-49f2-ac58-4ca463eb4c97","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"N. B. Proença, M. K. de Carli Silva, C. M. Sato, and L. Tunçel. A primal-dual extension of the Goemans–Williamson algorithm for the weighted fractional cut-covering problem.Mathematical Programming, p","work_id":"4e2951ab-71ed-4fbe-a097-492214c73b12","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"C. Bachoc, D. C. Gijswijt, A. Schrijver, and F. Vallentin. Invariant semidefinite programs. In M. F. Anjos and J. B. Lasserre, editors,Handbook on Semidefinite, Conic and Polynomial Optimization, page","work_id":"6c37bc45-0369-491e-82bb-616b4ab08cb3","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2004,"title":"Bailey.Association Schemes: Designed Experiments, Algebra, and Combi- natorics","work_id":"2d8c4922-50ce-4766-a0c7-e25f45c270f8","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"E. Bannai. An introduction to association schemes.Methods of Discrete Mathematics (eds. S. Löwe, F. Mazzocca, N. Melone and U. Ott), Quaderni di Mathematica, 5:1–70, 1999","work_id":"645bfb1b-2113-4e6e-aa70-2012d4ede2a0","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":32,"snapshot_sha256":"845df6b5985da8194f4f8bc8ace0b20ecca46751b54de677d8894359ec29b357","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"9f73249ac8d2b3029731144d49ef78c9657e45b576cc7b194db33dec39878d03"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}