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The Approximate Loebl-Komlos-Sos Conjecture III: The Finer Structure of LKS Graphs
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SYSNO ASEP 0474830 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The Approximate Loebl-Komlos-Sos Conjecture III: The Finer Structure of LKS Graphs Author(s) Hladký, J. (DE)
Komlós, J. (US)
Piguet, Diana (UIVT-O) RID, ORCID, SAI
Simonovits, M. (HU)
Stein, M. (CL)
Szemerédi, E. (HU)Source Title SIAM Journal on Discrete Mathematics. - : SIAM Society for Industrial and Applied Mathematics - ISSN 0895-4801
Roč. 31, č. 2 (2017), s. 1017-1071Number of pages 55 s. Language eng - English Country US - United States Keywords extremal graph theory ; Loebl–Komlós–Sós conjecture ; regularity lemma Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects 1M0545 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) GJ16-07822Y GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 UT WOS 000404770300023 EID SCOPUS 85022094119 DOI 10.1137/140982866 Annotation 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 $T$.
Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2018
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