{"paper":{"title":"Rapid mixing of Glauber dynamics for colorings below Vigoda's $11/6$ threshold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO","math.PR"],"primary_cat":"cs.DM","authors_text":"Guillem Perarnau, Luke Postle, Michelle Delcourt","submitted_at":"2018-04-11T14:38:23Z","abstract_excerpt":"A well-known conjecture in computer science and statistical physics is that Glauber dynamics on the set of $k$-colorings of a graph $G$ on $n$ vertices with maximum degree $\\Delta$ is rapidly mixing for $k \\geq \\Delta +2$. In FOCS 1999, Vigoda showed rapid mixing of flip dynamics with certain flip parameters on the set of proper $k$-colorings for $k > \\frac{11}{6}\\Delta$, implying rapid mixing for Glauber dynamics. In this paper, we obtain the first improvement beyond the $\\frac{11}{6}\\Delta$ barrier for general graphs by showing rapid mixing for $k > (\\frac{11}{6} - \\eta)\\Delta$ for some posi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04025","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"}