{"paper":{"title":"Counting independent sets and colorings on random regular bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Chao Liao, Jiabao Lin, Pinyan Lu, Zhenyu Mao","submitted_at":"2019-03-18T16:17:36Z","abstract_excerpt":"We give a fully polynomial-time approximation scheme (FPTAS) to count the number of independent sets on almost every $\\Delta$-regular bipartite graph if $\\Delta\\ge 53$. In the weighted case, for all sufficiently large integers $\\Delta$ and weight parameters $\\lambda=\\tilde\\Omega\\left(\\frac{1}{\\Delta}\\right)$, we also obtain an FPTAS on almost every $\\Delta$-regular bipartite graph. Our technique is based on the recent work of Jenssen, Keevash and Perkins (SODA, 2019) and we also apply it to confirm an open question raised there: For all $q\\ge 3$ and sufficiently large integers $\\Delta=\\Delta(q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07531","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"}