{"paper":{"title":"Tight Upper Bounds on Color Reversal by Local Inversions","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hitendra Kumar, Kumud Singh Porte, R. B. Sandeep","submitted_at":"2026-06-08T06:02:41Z","abstract_excerpt":"A bicoloration of a graph $G=(V,E)$ is a map $\\beta:V\\to\\{-1,1\\}$. A local inversion at a vertex $v$ complements the subgraph induced by the neighbors of $v$ and simultaneously reverses the colors of all neighbors of $v$. Sabidussi (Discrete Mathematics, 1987) showed that every bicolored graph on $n$ vertices without isolated vertices admits a color reversal using at most $6n+3$ local inversions, and that any two bicolorings of such a graph can be transformed into each other using at most $9n$ local inversions. Recently, Porte, Sandeep, and Santra (CALDAM 2026) improved these bounds to $4n-3$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09066","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/2606.09066/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"}