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    An approximate version of a conjecture of Aharoni and Berger

    Pokrovskiy, Alexey (2019) An approximate version of a conjecture of Aharoni and Berger. Technical Report. Birkbeck College, University of London, London, UK. (Unpublished)

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    Abstract

    Aharoni and Berger conjectured that in every proper edge-colouring of a bipartite multigraph by n colours with at least n + 1 edges of each colour there is a rainbow matching using every colour. This conjecture generalizes a longstanding problem of Brualdi and Stein about transversals in Latin squares. Here an approximate version of the Aharoni-Berger Conjecture is proved—it is shown that if there are at least n+o(n) edges of each colour in a proper n-edge-colouring of a bipartite multigraph then there is a rainbow matching using every colour.

    Metadata

    Item Type: Monograph (Technical Report)
    Additional Information: Birkbeck Pure Mathematics Preprint Series #52
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Maura Paterson
    Date Deposited: 15 Jun 2020 11:03
    Last Modified: 12 Feb 2021 19:17
    URI: https://eprints.bbk.ac.uk/id/eprint/32253

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