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    Linearly many rainbow trees in properly edge-coloured complete graphs

    Pokrovskiy, Alexey and Sudakov, B. (2018) Linearly many rainbow trees in properly edge-coloured complete graphs. Journal of Combinatorial Theory, Series B , ISSN 0095-8956.

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    A subgraph of an edge-coloured complete graph is called rainbow if all its edges have different colours. The study of rainbow decompositions has a long history, going back to the work of Euler on Latin squares. In this paper we discuss three problems about decomposing complete graphs into rainbow trees: the Brualdi-Hollingsworth Conjecture, Constantine's Conjecture, and the Kaneko-Kano-Suzuki Conjecture. We show that in every proper edge-colouring of Kn there are 10^{−6}n edge-disjoint spanning isomorphic rainbow trees. This simultaneously improves the best known bounds on all these conjectures. Using our method we also show that every properly (n−1)-edge-coloured Kn has n/9 edge-disjoint rainbow trees, giving further improvement on the Brualdi-Hollingsworth Conjecture.


    Item Type: Article
    Keyword(s) / Subject(s): Rainbow trees, Proper edge-colourings, Graph decompositions
    School: Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School
    Depositing User: Alexey Pokrovskiy
    Date Deposited: 12 Dec 2018 17:02
    Last Modified: 02 Aug 2023 17:47


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