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The approximate Loebl-Komlós-Sós Conjecture IV: Embedding techniques and the proof of the main result

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    0474808 - MÚ 2018 RIV US eng J - Článek v odborném periodiku
    Hladký, Jan - Komlós, J. - Piguet, Diana - Simonovits, M. - Stein, M. - Szemerédi, E.
    The approximate Loebl-Komlós-Sós Conjecture IV: Embedding techniques and the proof of the main result.
    SIAM Journal on Discrete Mathematics. Roč. 31, č. 2 (2017), s. 1072-1148. ISSN 0895-4801. E-ISSN 1095-7146
    Grant CEP: GA MŠk(CZ) 1M0545
    GRANT EU: European Commission(XE) 628974 - PAECIDM
    Institucionální podpora: RVO:67985840 ; RVO:67985807
    Klíčová slova: extremal graph theory * Loebl–Komlós–Sós conjecture * regularity lemma
    Obor OECD: Pure mathematics; Pure mathematics (UIVT-O)
    Impakt faktor: 0.717, rok: 2017
    http://epubs.siam.org/doi/10.1137/140982878

    This is the last 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 two papers of this series, we decomposed the host graph $G$ and found a suitable combinatorial structure inside the decomposition. In the third paper, we refined this structure and proved that any graph satisfying the conditions of the above approximate version of the Loebl-Komlós-Sós conjecture contains one of ten specific configurations. In this paper we embed the tree $T$ in each of the ten configurations.
    Trvalý link: http://hdl.handle.net/11104/0271759

     
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