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    Long directed rainbow cycles and rainbow spanning trees

    Benzing, F. and Pokrovskiy, Alexey and Sudakov, B. (2020) Long directed rainbow cycles and rainbow spanning trees. European Journal of Combinatorics 88 (103102), ISSN 0195-6698.

    1711.03772.pdf - Author's Accepted Manuscript
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    A subgraph of an edge-coloured graph is called rainbow if all its edges have different colours. The problem of finding rainbow subgraphs goes back to the work of Euler on transversals in Latin squares and was extensively studied since then. In this paper we consider two related questions concerning rainbow subgraphs of complete, edge-coloured graphs and digraphs. In the first part, we show that every properly edge-coloured complete directed graph contains a directed rainbow cycle of length n−O(n^4/5). This is motivated by an old problem of Hahn and improves a result of Gyarfas and Sarkozy. In the second part, we show that any tree T on n vertices with maximum degree Δ(T)≤βn/logn has a rainbow embedding into a properly edge-coloured Kn provided that every colour appears at most αn times and α,β are sufficiently small constants.


    Item Type: Article
    School: Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School
    Depositing User: Alexey Pokrovskiy
    Date Deposited: 15 May 2019 12:00
    Last Modified: 02 Aug 2023 17:51


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