{"paper":{"title":"Minimum vertex cover problems on random hypergraphs: replica symmetric solution and a leaf removal algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Koji Hukushima, Satoshi Takabe","submitted_at":"2013-01-24T12:24:06Z","abstract_excerpt":"We study minimum vertex cover problems on random \\alpha-uniform hypergraphs using two different approaches, a replica method in statistical mechanics of random systems and a leaf removal algorithm. It is found that there exists a phase transition at the critical average degree e/(\\alpha-1). Below the critical degree, a replica symmetric ansatz in the statistical-mechanical method holdsand the algorithm estimates a solution of the problem which coincide with that by the replica method. In contrast, above the critical degree, the replica symmetric solution becomes unstable and these methods fail"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5769","kind":"arxiv","version":1},"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"}