{"paper":{"title":"Improved bounds on the b-chromatic number using the independence and chromatic numbers","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Manouchehr Zaker","submitted_at":"2026-06-05T17:13:10Z","abstract_excerpt":"A b-coloring of a graph $G$ is a proper vertex coloring where each color class contains at least one vertex (a b-vertex) adjacent to a vertex in every other color class. The maximum number of colors in such a coloring is the b-chromatic number, ${\\rm b}(G)$. A ${\\rm b}^{\\ast}$-coloring is a variation in which a b-vertex is adjacent to a b-vertex in every other color class. We employ the ${\\rm b}^{\\ast}$-coloring to prove that any $n$-vertex graph $G$ with independence number at most $t$ satisfies ${\\rm b}(G) \\leq ((t-1)n+t\\chi(G))/(2t-1)$. This bound extends the bounds of Kouider and Zaker (20"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07461","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/2606.07461/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"}