{"paper":{"title":"On the b-chromatic number of the Cartesian product of two complete graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Artur Mesquita Barbosa, Fr\\'ed\\'eric Maffray","submitted_at":"2015-04-08T14:09:19Z","abstract_excerpt":"A b-coloring of a graph $G$ is a coloring of its vertices such that every color class contains a vertex that has neighbors in all other classes. The b-chromatic number of $G$ is the largest integer $k$ such that $G$ has a b-coloring with $k$ colors. Javadi and Omoomi (\"On b-coloring of cartesian product of graphs\", Ars Combinatoria 107 (2012) 521-536) proved that the b-chromatic number of $K_n \\times K_n$ (the Cartesian product of two complete graphs on $n$ vertices) is in the set $\\{2n-3, 2n-2\\}$ and conjectured that the exact value is $2n-3$ for all $n \\ge 5$. We give counterexamples to this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01975","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"}