{"paper":{"title":"On some upper bounds on the fractional chromatic number of weighted graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Ashwin Ganesan","submitted_at":"2010-01-18T13:21:04Z","abstract_excerpt":"Given a weighted graph $G_\\bx$, where $(x(v): v \\in V)$ is a non-negative, real-valued weight assigned to the vertices of G, let $B(G_\\bx)$ be an upper bound on the fractional chromatic number of the weighted graph $G_\\bx$; so $\\chi_f(G_\\bx) \\le B(G_\\bx)$. To investigate the worst-case performance of the upper bound $B$, we study the graph invariant $$\\beta(G) = \\sup_{\\bx \\ne 0} \\frac{B(G_\\bx)}{\\chi_f(G_\\bx)}.$$\n  \\noindent This invariant is examined for various upper bounds $B$ on the fractional chromatic number. In some important cases, this graph invariant is shown to be related to the size"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3053","kind":"arxiv","version":4},"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"}