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Ramsey goodness of trees in random graphs

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F23%3A00561499" target="_blank" >RIV/67985807:_____/23:00561499 - isvavai.cz</a>

  • Result on the web

    <a href="https://dx.doi.org/10.1002/rsa.21124" target="_blank" >https://dx.doi.org/10.1002/rsa.21124</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1002/rsa.21124" target="_blank" >10.1002/rsa.21124</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Ramsey goodness of trees in random graphs

  • Original language description

    For graphs G, H and a family of graphs., we write G ->(H,P) to denote that every blue-red coloring of the edges of G contains either a blue copy of H, or a red copy of each F is an element of P For integers n and D, let tau(n, D) denote the family of all trees with n edges and maximum degree atmostD. We prove that for each r, D >= 2, there exist constants C, C' > 0 such that if p >= Cn(-2/(r+2)) and N >= rn + C'/p, then G(N, p)->(Kr+ 1, tau(n, D)) with high probability. This is a random version of a well-known result of Chvatal from 1977. The proof combines a stability argument with the embedding of trees in expander graphs. Furthermore, the proof of the stability result is based on a sparse random analogue of the Erd.os-Sos conjecture for trees with linear size and bounded maximum degree, which may 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

    <a href="/en/project/GJ20-27757Y" target="_blank" >GJ20-27757Y: Random discrete structures</a><br>

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2023

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Random Structures and Algorithms

  • ISSN

    1042-9832

  • e-ISSN

    1098-2418

  • Volume of the periodical

    62

  • Issue of the periodical within the volume

    4

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    30

  • Pages from-to

    761-790

  • UT code for WoS article

    000880355700001

  • EID of the result in the Scopus database

    2-s2.0-85148345421