{"paper":{"title":"The Minrank of Random Graphs over Arbitrary Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Adva Mond, Frank Mousset, Igor Balla, Lior Gishboliner, Noga Alon","submitted_at":"2018-09-06T08:23:05Z","abstract_excerpt":"The minrank of a graph $G$ on the set of vertices $[n]$ over a field $\\mathbb{F}$ is the minimum possible rank of a matrix $M\\in\\mathbb{F}^{n\\times n}$ with nonzero diagonal entries such that $M_{i,j}=0$ whenever $i$ and $j$ are distinct nonadjacent vertices of $G$. This notion, over the real field, arises in the study of the Lov\\'asz theta function of a graph. We obtain tight bounds for the typical minrank of the binomial random graph $G(n,p)$ over any finite or infinite field, showing that for every field $\\mathbb{F}=\\mathbb F(n)$ and every $p=p(n)$ satisfying $n^{-1} \\leq p \\leq 1-n^{-0.99}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01873","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"}