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The approximate Loebl-Komlós-Sós Conjecture II: The rough structure of LKS graphs

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F17%3A00474809" target="_blank" >RIV/67985807:_____/17:00474809 - isvavai.cz</a>

  • Alternative codes found

    RIV/67985840:_____/17:00474809

  • Result on the web

    <a href="http://dx.doi.org/10.1137/140982854" target="_blank" >http://dx.doi.org/10.1137/140982854</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1137/140982854" target="_blank" >10.1137/140982854</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    The approximate Loebl-Komlós-Sós Conjecture II: The rough structure of LKS graphs

  • Original language description

    This is the second of a series of four papers in which we prove the following relaxation of the Loebl-Komlós-Sós conjecture: For every $alpha>0$ there exists a number $k_0$ such that for every $k>k_0$, every $n$-vertex graph $G$ with at least $(0.5+alpha)n$ vertices of degree at least $(1+alpha)k$ contains each tree $T$ of order $k$ as a subgraph. In the first paper of this series, we gave a decomposition of the graph $G$ into several parts of different characteristics, this decomposition might be viewed as an analogue of a regular partition for sparse graphs. In the present paper, we find a combinatorial structure inside this decomposition. In the third and fourth papers, we refine the structure and use it for embedding the tree $T$.

  • 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/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2017

  • 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

    31

  • Issue of the periodical within the volume

    2

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    34

  • Pages from-to

    983-1016

  • UT code for WoS article

    000404770300022

  • EID of the result in the Scopus database

    2-s2.0-85021890019