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It was recently proved by Guo and Jerrum (2017) that the Swendsen-Wang dynamics has polynomial mixing time on any graph at all temperatures, yet there are few results providing $o(|V|)$ upper bounds on its convergence time.\n  We prove fast convergence of the Swendsen-Wang dynamics on "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1806.04602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-06-12T15:23:29Z","cross_cats_sorted":["cs.DS","math-ph","math.MP","math.PR"],"title_canon_sha256":"6ed8e4b103947f7c3a44e1cee9c596ee41602de31cff5ec29c40693fddce6e6f","abstract_canon_sha256":"aee4ddc8720d2c15be7979745d14cd1e3820c135e75950756db5ac9afaadbbef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:33.266465Z","signature_b64":"HZQy386OJLx7YKTetsBOnmrfZBDF6bXoBcMNF/58f6rzoSTYiKxXtw8L08O3CtHHv4PAg6xVL/WRbcckY4rxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18cb192083e152693289c51cdc58550da1e5fbf19a626087594efb559ec03d90","last_reissued_at":"2026-05-18T00:13:33.265919Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:33.265919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Swendsen-Wang Dynamics for General Graphs in the Tree Uniqueness Region","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math-ph","math.MP","math.PR"],"primary_cat":"cs.DM","authors_text":"Antonio Blanca, Eric Vigoda, Zongchen Chen","submitted_at":"2018-06-12T15:23:29Z","abstract_excerpt":"The Swendsen-Wang dynamics is a popular algorithm for sampling from the Gibbs distribution for the ferromagnetic Ising model on a graph $G=(V,E)$. 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