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This result was later extended by Bartier, Bousquet, and Heinrich, who proved that $\\mathcal{R}_5(G)$ also has linear diameter.\n  In this paper, we show that for each $\\ell\\geq 5$, the $\\ell$-reconfiguration graphs of $K_{2,3}$"},"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":"2605.31225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-29T12:28:40Z","cross_cats_sorted":[],"title_canon_sha256":"e28f325b9d7eab5869b874b26d4af76549170729479396edadaa992f6a9d998e","abstract_canon_sha256":"18fa0e87ee18ec6f0f0fee5098d17aa22f5748eda93cbe45501fccb3c0391962"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T01:04:04.844001Z","signature_b64":"JyQ7iDQTj8DimtIUXuvWezTvGXA1r53phxPDNGfJqJ5p4VMOXsetGDWODe/pplJMZl35yQkGkVqub0NxufzVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"648f300b84f986cff00d05d5434594b785482f12ffcc92f152d229e1b28799da","last_reissued_at":"2026-06-01T01:04:04.843176Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T01:04:04.843176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reconfiguration graphs of $K_{2,3}$-minor-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hui Lei, Ruijuan Gu, Susu Wang, Yulai Ma, Zhaoxiang Li","submitted_at":"2026-05-29T12:28:40Z","abstract_excerpt":"The $\\ell$-reconfiguration graph of a graph $G$, denoted by $\\mathcal{R}_{\\ell}(G)$, is the graph whose vertices are the proper $\\ell$-colorings of $G$, with an edge between two colorings if they differ in color on exactly one vertex. 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