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Any graph is $(tw+2)$-mixing, where $tw$ is the treewidth of the graph (Cereceda 2006). We prove that the shortest sequence between any two $(tw+2)$-colorings is at most quadratic, a problem left open in Bonamy et al. (2012).\n  Jerrum proved that any graph is $k$-mixing if $k$ is at least the maximum degree plus two. We improve Jerrum's b"},"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":"1302.3486","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-02-14T17:43:07Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a96fb3972f0c25e128e7efe8f26a4320e5c4ec52fb52a77cd17b62d8497b266b","abstract_canon_sha256":"ec7c52ff648a5257d45c68b270b00fb01cbc8cb44471ae6b9399c12c6166b7d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:38.459821Z","signature_b64":"I1ipa1uLfQFxLF2Y+kCBI5eg9caUD+Zb8c+5NbLv9pKoKoMYhSVPtviS6Op3v8+5RvYJ418MeyseClN2EQ9vDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1511cd9fb2e199903a555a92aa31ba52ce47d7cba1fe84e1c71b189bad89ac3","last_reissued_at":"2026-05-18T03:33:38.459358Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:38.459358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recoloring bounded treewidth graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Marthe Bonamy, Nicolas Bousquet","submitted_at":"2013-02-14T17:43:07Z","abstract_excerpt":"Let $k$ be an integer. Two vertex $k$-colorings of a graph are \\emph{adjacent} if they differ on exactly one vertex. A graph is \\emph{$k$-mixing} if any proper $k$-coloring can be transformed into any other through a sequence of adjacent proper $k$-colorings. Any graph is $(tw+2)$-mixing, where $tw$ is the treewidth of the graph (Cereceda 2006). We prove that the shortest sequence between any two $(tw+2)$-colorings is at most quadratic, a problem left open in Bonamy et al. (2012).\n  Jerrum proved that any graph is $k$-mixing if $k$ is at least the maximum degree plus two. 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