{"paper":{"title":"New NP-hardness results for 3-Coloring and 2-to-1 Label Cover","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"John Wright, Li-Yang Tan, Per Austrin, Ryan O'Donnell","submitted_at":"2012-10-20T19:34:22Z","abstract_excerpt":"We show that given a 3-colorable graph, it is NP-hard to find a 3-coloring with $(16/17 + \\eps)$ of the edges bichromatic. In a related result, we show that given a satisfiable instance of the 2-to-1 Label Cover problem, it is NP-hard to find a $(23/24 + \\eps)$-satisfying assignment."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5648","kind":"arxiv","version":2},"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"}