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KNESER RANKS OF RANDOM GRAPHS AND MINIMUM DIFFERENCE REPRESENTATIONS

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10387686" target="_blank" >RIV/00216208:11320/18:10387686 - isvavai.cz</a>

  • Result on the web

    <a href="https://doi.org/10.1137/17M1114703" target="_blank" >https://doi.org/10.1137/17M1114703</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1137/17M1114703" target="_blank" >10.1137/17M1114703</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    KNESER RANKS OF RANDOM GRAPHS AND MINIMUM DIFFERENCE REPRESENTATIONS

  • Original language description

    Every graph G = (V;E) is an induced subgraph of some Kneser graph of rank k, i.e., there is an assignment of (distinct) k-sets v -&gt; A(v) to the vertices v is an element of V such that A(u) and A(v) are disjoint if and only if uv is an element of E. The smallest such k is called the Kneser rank of G and denoted by fK(neser) (G). As an application of a result of Frieze and Reed concerning the clique cover number of random graphs we show that for constant 0 &lt; p &lt; 1 there exist constants c(i) = c(i) (p) &gt; 0, i = 1; 2, such that G is an element of G (n; p) satisfies with high probability c(1)n/(log n) &lt; fK(neser) (G) &lt; c(2)n= (log n) : We apply this for other graph representations defined by Boros, Gurvich, and Meshulam. A k-mindifference representation of a graph G is an assignment of a set A(i) to each vertex i is an element of V (G) such that ij is an element of E (G) double left right arrow min {vertical bar Ai A(i) vertical bar, vertical bar A(j) A(i vertical bar)vertical bar}&gt;= k: The smallest k such that there exists a k-mindi ff erence representation of G is denoted by fmin (G). Balogh and Prince proved in 2009 that for every k there is a graph G with f(min) (G) &gt;= k. We prove that there are constants c &apos;&apos;(1); c &apos;&apos;(2) &gt; 0 such that c &apos;&apos;(1)n /(log n) &lt; f(min) (G) &lt; c &apos;&apos;(2) n / (log n) holds for almost all bipartite graphs G on n + n vertices.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Result continuities

  • Project

    <a href="/en/project/GJ16-01602Y" target="_blank" >GJ16-01602Y: Topological and geometric approaches to classes of permutations and graph properties</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2018

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    SIAM Journal on Discrete Mathematics

  • ISSN

    0895-4801

  • e-ISSN

  • Volume of the periodical

    32

  • Issue of the periodical within the volume

    2

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    13

  • Pages from-to

    1016-1028

  • UT code for WoS article

    000436975900014

  • EID of the result in the Scopus database

    2-s2.0-85049599616