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    An approximate version of a conjecture of Aharoni and Berger

    Pokrovskiy, Alexey (2018) An approximate version of a conjecture of Aharoni and Berger. Advances in Mathematics 333 , pp. 1197-1241. ISSN 0001-8708.

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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 AharoniBerger 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: Article
    Keyword(s) / Subject(s): Latin squares, Rainbow matchings, Connectedness
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Alexey Pokrovskiy
    Date Deposited: 12 Dec 2018 16:51
    Last Modified: 12 Feb 2021 06:59
    URI: https://eprints.bbk.ac.uk/id/eprint/25436

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