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    Nearly-linear monotone paths in edge-ordered graphs

    Bucic, M. and Kwan, M. and Pokrovskiy, Alexey and Sudakov, B. and Tran, T. and Wagner, A.Z. (2020) Nearly-linear monotone paths in edge-ordered graphs. Israel Journal of Mathematics 238 , pp. 663-685. ISSN 0021-2172.

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    Abstract

    How long a monotone path can one always find in any edge-ordering of the complete graph Kn? This appealing question was first asked by Chvátal and Komlós in 1971, and has since attracted the attention of many researchers, inspiring a variety of related problems. The prevailing conjecture is that one can always find a monotone path of linear length, but until now the best known lower bound was n^2/3−o(1). In this paper we almost close this gap, proving that any edge-ordering of the complete graph contains a monotone path of length n^1−o(1).

    Metadata

    Item Type: Article
    Additional Information: The final publication is available at Springer via the link above.
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Alexey Pokrovskiy
    Date Deposited: 20 Jan 2020 13:23
    Last Modified: 07 Jul 2021 00:10
    URI: https://eprints.bbk.ac.uk/id/eprint/30606

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