{"paper":{"title":"On the strong chromatic number of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maria Axenovich, Ryan R. Martin","submitted_at":"2016-05-21T02:27:02Z","abstract_excerpt":"The strong chromatic number, $\\chi_S(G)$, of an $n$-vertex graph $G$ is the smallest number $k$ such that after adding $k\\lceil n/k\\rceil-n$ isolated vertices to $G$ and considering {\\bf any} partition of the vertices of the resulting graph into disjoint subsets $V_1, \\ldots, V_{\\lceil n/k\\rceil}$ of size $k$ each, one can find a proper $k$-vertex-coloring of the graph such that each part $V_i$, $i=1, \\ldots, \\lceil n/k\\rceil$, contains exactly one vertex of each color.\n  For any graph $G$ with maximum degree $\\Delta$, it is easy to see that $\\chi_S(G)\\geq\\Delta+1$. Recently, Haxell proved tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06574","kind":"arxiv","version":2},"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"}