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    Highly linked tournaments

    Pokrovskiy, Alexey (2015) Highly linked tournaments. Journal of Combinatorial Theory, Series B 115 , pp. 339-347. ISSN 0095-8956.

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    A (possibly directed) graph is k-linked if for any two disjoint sets of vertices {x1,…,xk} and {y1,…,yk} there are vertex disjoint paths P1,…,Pk such that Pi goes from xi to yi. A theorem of Bollobás and Thomason says that every 22k-connected (undirected) graph is k-linked. It is desirable to obtain analogues for directed graphs as well. Although Thomassen showed that the Bollobás-Thomason Theorem does not hold for general directed graphs, he proved an analogue of the theorem for tournaments - there is a function f(k) such that every strongly f(k)-connected tournament is k-linked. The bound on f(k) was reduced to O(klogk) by Kühn, Lapinskas, Osthus, and Patel, who also conjectured that a linear bound should hold. We prove this conjecture, by showing that every strongly 452k-connected tournament is k-linked.


    Item Type: Article
    Keyword(s) / Subject(s): Connectivity of tournaments, Linkedness, Linkage structures
    School: Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School
    Depositing User: Alexey Pokrovskiy
    Date Deposited: 21 Jan 2019 15:44
    Last Modified: 02 Aug 2023 17:47


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