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Localized Codegree Conditions for Tight Hamilton Cycles in 3-Uniform Hypergraphs

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F22%3A00556853" target="_blank" >RIV/67985807:_____/22:00556853 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1137/21M1408531" target="_blank" >http://dx.doi.org/10.1137/21M1408531</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1137/21M1408531" target="_blank" >10.1137/21M1408531</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Localized Codegree Conditions for Tight Hamilton Cycles in 3-Uniform Hypergraphs

  • Original language description

    We study sufficient conditions for the existence of Hamilton cycles in uniformly dense 3-uniform hypergraphs. Problems of this type were first considered by Lenz, Mubayi, and Mycroft for loose Hamilton cycles, and Aigner-Horev and Levy considered them for tight Hamilton cycles for a fairly strong notion of uniformly dense hypergraphs. We focus on tight cycles and obtain optimal results for a weaker notion of uniformly dense hypergraphs. We show that if an n-vertex 3-uniform hypergraph H = (V, E) has the property that for any set of vertices X and for any collection P of pairs of vertices, the number of hyperedges composed by a pair belonging to P and one vertex from X is at least (1/4 +o(1))vertical bar X vertical bar vertical bar P vertical bar- o(vertical bar V vertical bar(3)) and H has minimum vertex degree at least Omega(vertical bar V vertical bar(2)), then H contains a tight Hamilton cycle. A probabilistic construction shows that the constant 1/4 is optimal in this context.

  • 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

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2022

  • 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

    1095-7146

  • Volume of the periodical

    36

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    23

  • Pages from-to

    147-169

  • UT code for WoS article

    000778502000008

  • EID of the result in the Scopus database

    2-s2.0-85128397699