{"paper":{"title":"On The b-Chromatic Number of Regular Bounded Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amine El Sahili, Maidoun Mortada, Mekkia Kouider","submitted_at":"2013-02-18T10:17:29Z","abstract_excerpt":"A $b$-coloring of a graph is a proper coloring such that every color class contains a vertex adjacent to at least one vertex in each of the other color classes. The $b$-chromatic number of a graph $G$, denoted by $b(G)$, is the maximum integer $k$ such that $G$ admits a $b$-coloring with $k$ colors. El Sahili and Kouider conjectured that $b(G)=d+1$ for $d$-regular graph with girth 5, $d\\geq4$. In this paper, we prove that this conjecture holds for $d$-regular graph with at least $d^3+d$ vertices. More precisely we show that $b(G)=d+$1 for $d$-regular graph with at least $d^3+d$ vertices and co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4209","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":""},"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"}