{"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. For any graph $G$ of treewidth at most $2$, Bousquet and Perarnau showed that $\\mathcal{R}_\\ell(G)$ has linear diameter for $\\ell\\geq 6$. 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 $K_{2,3}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31225","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.31225/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}