{"paper":{"title":"Expected values of parameters associated with the minimum rank of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bryan Shader, Leslie Hogben, Ryan R. Martin, Tracy Hall","submitted_at":"2016-05-18T18:43:32Z","abstract_excerpt":"We investigate the expected value of various graph parameters associated with the minimum rank of a graph, including minimum rank/maximum nullity and related Colin de Verdi\\`ere-type parameters. Let $G(v,p)$ denote the usual Erd\\H{o}s-R\\'enyi random graph on $v$ vertices with edge probability $p$. We obtain bounds for the expected value of the random variables ${\\rm mr}(G(v,p))$, ${\\rm M}(G(v,p))$, $\\nu(G(v,p))$ and $\\xi(G(v,p))$, which yield bounds on the average values of these parameters over all labeled graphs of order $v$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05692","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"}