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A Turán-type theorem for large-distance graphs in Euclidean spaces, and related isodiametric problems

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00543158" target="_blank" >RIV/67985840:_____/21:00543158 - isvavai.cz</a>

  • Alternative codes found

    RIV/00216208:11320/21:10422533

  • Result on the web

    <a href="https://doi.org/10.1007/s00454-020-00183-2" target="_blank" >https://doi.org/10.1007/s00454-020-00183-2</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/s00454-020-00183-2" target="_blank" >10.1007/s00454-020-00183-2</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    A Turán-type theorem for large-distance graphs in Euclidean spaces, and related isodiametric problems

  • Original language description

    Given a measurable set A⊂R^d we consider the 'large-distance graph' G_A, on the ground set A, in which each pair of points from A whose distance is bigger than 2 forms an edge. We consider the problems of maximizing the 2d-dimensional Lebesgue measure of the edge set as well as the d-dimensional Lebesgue measure of the vertex set of a large-distance graph in the d-dimensional Euclidean space that contains no copies of a complete graph on k vertices. The former problem may be seen as a continuous analogue of Turán's classical graph theorem, and the latter as a graph-theoretic analogue of the classical isodiametric problem. Our main result yields an analogue of Mantel's theorem for large-distance graphs. Our approach employs an isodiametric inequality in an annulus, which might be of independent interest.

  • 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

    10101 - Pure mathematics

Result continuities

  • Project

    Result was created during the realization of more than one project. More information in the Projects tab.

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2021

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Discrete & Computational Geometry

  • ISSN

    0179-5376

  • e-ISSN

    1432-0444

  • Volume of the periodical

    66

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    20

  • Pages from-to

    281-300

  • UT code for WoS article

    000516374700001

  • EID of the result in the Scopus database

    2-s2.0-85107553012