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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.

    1809.01468.pdf - Author's Accepted Manuscript

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    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).


    Item Type: Article
    Additional Information: The final publication is available at Springer via the link above.
    School: Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School
    Depositing User: Alexey Pokrovskiy
    Date Deposited: 20 Jan 2020 13:23
    Last Modified: 02 Aug 2023 17:56


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