{"paper":{"title":"Sampling colorings almost uniformly in sparse random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Chihao Zhang, Yitong Yin","submitted_at":"2015-03-11T14:31:49Z","abstract_excerpt":"The problem of sampling proper $q$-colorings from uniform distribution has been extensively studied. Most of existing samplers require $q\\ge \\alpha \\Delta+\\beta$ for some constants $\\alpha$ and $\\beta$, where $\\Delta$ is the maximum degree of the graph. The problem becomes more challenging when the underlying graph has unbounded degree since even the decision of $q$-colorability becomes nontrivial in this situation. The Erd\\H{o}s-R\\'{e}nyi random graph $\\mathcal{G}(n,d/n)$ is a typical class of such graphs and has received a lot of recent attention. In this case, the performance of a sampler i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03351","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"}