Matches in SemOpenAlex for { <https://semopenalex.org/work/W2983826328> ?p ?o ?g. }
Showing items 1 to 81 of
81
with 100 items per page.
- W2983826328 endingPage "77" @default.
- W2983826328 startingPage "63" @default.
- W2983826328 abstract "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 Mi,j = 0 whenever i and j are distinct nonadjacent vertices of G. This notion, over the real field, arises in the study of the Lovász 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 ≤ p ≤ 1 - n-0.99, the minrank of G = G(n, p) over $$mathbb{F}$$ is $$Theta(frac{n {rm{log}}(1/p)}{{rm{log}} n})$$ with high probability. The result for the real field settles a problem raised by Knuth in 1994. The proof combines a recent argument of Golovnev, Regev and Weinstein, who proved the above result for finite fields of size at most nO(1), with tools from linear algebra, including an estimate of Rónyai, Babai and Ganapathy for the number of zero-patterns of a sequence of polynomials." @default.
- W2983826328 created "2019-11-22" @default.
- W2983826328 creator A5033968775 @default.
- W2983826328 creator A5055318466 @default.
- W2983826328 creator A5083469386 @default.
- W2983826328 creator A5084893376 @default.
- W2983826328 creator A5088239069 @default.
- W2983826328 date "2019-11-04" @default.
- W2983826328 modified "2023-09-24" @default.
- W2983826328 title "The minrank of random graphs over arbitrary fields" @default.
- W2983826328 cites W1543186430 @default.
- W2983826328 cites W1548134571 @default.
- W2983826328 cites W1966169258 @default.
- W2983826328 cites W2030052209 @default.
- W2983826328 cites W2056125869 @default.
- W2983826328 cites W2078289947 @default.
- W2983826328 cites W2082249316 @default.
- W2983826328 cites W2130507035 @default.
- W2983826328 cites W3104596032 @default.
- W2983826328 cites W3123198802 @default.
- W2983826328 cites W51435562 @default.
- W2983826328 doi "https://doi.org/10.1007/s11856-019-1945-8" @default.
- W2983826328 hasPublicationYear "2019" @default.
- W2983826328 type Work @default.
- W2983826328 sameAs 2983826328 @default.
- W2983826328 citedByCount "3" @default.
- W2983826328 countsByYear W29838263282020 @default.
- W2983826328 countsByYear W29838263282021 @default.
- W2983826328 crossrefType "journal-article" @default.
- W2983826328 hasAuthorship W2983826328A5033968775 @default.
- W2983826328 hasAuthorship W2983826328A5055318466 @default.
- W2983826328 hasAuthorship W2983826328A5083469386 @default.
- W2983826328 hasAuthorship W2983826328A5084893376 @default.
- W2983826328 hasAuthorship W2983826328A5088239069 @default.
- W2983826328 hasBestOaLocation W29838263282 @default.
- W2983826328 hasConcept C105795698 @default.
- W2983826328 hasConcept C114614502 @default.
- W2983826328 hasConcept C118615104 @default.
- W2983826328 hasConcept C130367717 @default.
- W2983826328 hasConcept C132525143 @default.
- W2983826328 hasConcept C202444582 @default.
- W2983826328 hasConcept C2524010 @default.
- W2983826328 hasConcept C2781315470 @default.
- W2983826328 hasConcept C33923547 @default.
- W2983826328 hasConcept C34718186 @default.
- W2983826328 hasConcept C77926391 @default.
- W2983826328 hasConcept C9652623 @default.
- W2983826328 hasConceptScore W2983826328C105795698 @default.
- W2983826328 hasConceptScore W2983826328C114614502 @default.
- W2983826328 hasConceptScore W2983826328C118615104 @default.
- W2983826328 hasConceptScore W2983826328C130367717 @default.
- W2983826328 hasConceptScore W2983826328C132525143 @default.
- W2983826328 hasConceptScore W2983826328C202444582 @default.
- W2983826328 hasConceptScore W2983826328C2524010 @default.
- W2983826328 hasConceptScore W2983826328C2781315470 @default.
- W2983826328 hasConceptScore W2983826328C33923547 @default.
- W2983826328 hasConceptScore W2983826328C34718186 @default.
- W2983826328 hasConceptScore W2983826328C77926391 @default.
- W2983826328 hasConceptScore W2983826328C9652623 @default.
- W2983826328 hasIssue "1" @default.
- W2983826328 hasLocation W29838263281 @default.
- W2983826328 hasLocation W29838263282 @default.
- W2983826328 hasOpenAccess W2983826328 @default.
- W2983826328 hasPrimaryLocation W29838263281 @default.
- W2983826328 hasRelatedWork W1587332544 @default.
- W2983826328 hasRelatedWork W2024600207 @default.
- W2983826328 hasRelatedWork W2079118119 @default.
- W2983826328 hasRelatedWork W2143011322 @default.
- W2983826328 hasRelatedWork W2145476401 @default.
- W2983826328 hasRelatedWork W2473415529 @default.
- W2983826328 hasRelatedWork W2613826160 @default.
- W2983826328 hasRelatedWork W2951403411 @default.
- W2983826328 hasRelatedWork W2963638677 @default.
- W2983826328 hasRelatedWork W379674649 @default.
- W2983826328 hasVolume "235" @default.
- W2983826328 isParatext "false" @default.
- W2983826328 isRetracted "false" @default.
- W2983826328 magId "2983826328" @default.
- W2983826328 workType "article" @default.