{"paper":{"title":"More Tales of Hoffman: bounds for the vector chromatic number of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Clive Elphick, David Anekstein, Pawel Wocjan","submitted_at":"2018-12-06T15:43:17Z","abstract_excerpt":"Let $\\chi(G)$ denote the chromatic number of a graph and $\\chi_v(G)$ denote the vector chromatic number. For all graphs $\\chi_v(G) \\le \\chi(G)$ and for some graphs $\\chi_v(G) \\ll \\chi(G)$. Galtman proved that Hoffman's well-known lower bound for $\\chi(G)$ is in fact a lower bound for $\\chi_v(G)$. We prove that two more spectral lower bounds for $\\chi(G)$ are also lower bounds for $\\chi_v(G)$. We then use one of these bounds to derive a new characterization of $\\chi_v(G)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02613","kind":"arxiv","version":3},"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/1812.02613/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"}