{"paper":{"title":"Practical Experience with Stable Set and Coloring Relaxations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Dunja Pucher, Franz Rendl","submitted_at":"2024-01-30T14:52:01Z","abstract_excerpt":"The stable set problem and the graph coloring problem are classes of NP-hard optimization problems on graphs. It is well known that even near-optimal solutions for these problems are difficult to find in polynomial time. The Lov\\'asz theta function, introduced by Lov\\'asz in the late 1970s, provides a powerful tool in the study of these problems. It can be expressed as the optimal value of a semidefinite program and serves as a relaxation for both problems. Over the years, considerable effort has been devoted to investigating additional cutting planes to strengthen these relaxations. In our wo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.17069","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.17069/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}