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A Local Approach to the Erdős-Sós Conjecture

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    0504792 - ÚI 2020 RIV US eng J - Journal Article
    Rozhoň, Václav
    A Local Approach to the Erdős-Sós Conjecture.
    SIAM Journal on Discrete Mathematics. Roč. 33, č. 2 (2019), s. 643-664. ISSN 0895-4801. E-ISSN 1095-7146
    R&D Projects: GA ČR GJ16-07822Y
    Institutional support: RVO:67985807
    Keywords : Erdős-Sós conjecture * embedding of trees * extremal combinatorics
    OECD category: Pure mathematics
    Impact factor: 0.750, year: 2019
    Method of publishing: Limited access

    A famous conjecture of Erdős-Sós states that every graph with average degree more than k-1 contains all trees with k edges as subgraphs. We prove that the Erdős-Sós conjecture holds approximately, if the size of the embedded tree is linear in the size of the graph, and the maximum degree of the tree is sublinear.
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