{"paper":{"title":"Improved Bounds for Randomly Sampling Colorings via Linear Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math-ph","math.MP","math.PR"],"primary_cat":"cs.DS","authors_text":"Ankur Moitra, Guillem Perarnau, Luke Postle, Michelle Delcourt, Sitan Chen","submitted_at":"2018-10-30T19:51:29Z","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 $k\\ge\\Delta+2$. In FOCS 1999, Vigoda showed that the flip dynamics (and therefore also Glauber dynamics) is rapidly mixing for any $k>\\frac{11}{6}\\Delta$. It turns out that there is a natural barrier at $\\frac{11}{6}$, below which there is no one-step coupling that is contractive with respect to the Hamming metric, even for the flip dynamics.\n  We use linear programming and duality arguments to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12980","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"}