The Approximate Loebl-Komlos-Sos Conjecture III: The Finer Structure of LKS Graphs
Result description
This is the third 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 $(frac12+alpha)n$ vertices of degree at least $(1+alpha)k$ contains each tree $T$ of order $k$ as a subgraph. In the first paper of the series, we gave a decomposition of the graph $G$ into several parts of different characteristics. In the second paper, we found a combinatorial structure inside the decomposition. In this paper, we will give a refinement of this structure. In the fourth paper, the refined structure will be used for embedding the tree $T$.n
Keywords
extremal graph theoryLoebl–Komlós–Sós conjectureregularity lemma
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
The Approximate Loebl-Komlos-Sos Conjecture III: The Finer Structure of LKS Graphs
Original language description
This is the third 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 $(frac12+alpha)n$ vertices of degree at least $(1+alpha)k$ contains each tree $T$ of order $k$ as a subgraph. In the first paper of the series, we gave a decomposition of the graph $G$ into several parts of different characteristics. In the second paper, we found a combinatorial structure inside the decomposition. In this paper, we will give a refinement of this structure. In the fourth paper, the refined structure will be used for embedding the tree $T$.n
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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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
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
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
55
Pages from-to
1017-1071
UT code for WoS article
000404770300023
EID of the result in the Scopus database
2-s2.0-85022094119
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Pure mathematics
Year of implementation
2017