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

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>

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
—

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

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

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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