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    Edge disjoint Hamilton cycles in sparse random graphs of minimum degree at least \emphk

    Bollobas, B. and Cooper, C. and Fenner, Trevor and Frieze, A.M. (2000) Edge disjoint Hamilton cycles in sparse random graphs of minimum degree at least \emphk. Journal of Graph Theory 34 (1), pp. 42-59. ISSN 0364-9024.

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    Abstract

    Let Gn,m,k denote the space of simple graphs with n vertices, m edges, and minimum degree at least k, each graph G being equiprobable. Let G have property Ak, if G contains ⌊(k − 1)/2⌋ edge disjoint Hamilton cycles, and, if k is even, a further edge disjoint matching of size ⌊n/2⌋. We prove that, for k ≥ 3, there is a constant Ck such that if 2m ≥ Ckn then Ak occurs in Gn,m,k with probability tending to 1 as n → ∞.

    Metadata

    Item Type: Article
    School: School of Business, Economics & Informatics > Computer Science and Information Systems
    Depositing User: Sarah Hall
    Date Deposited: 16 Mar 2021 20:31
    Last Modified: 16 Mar 2021 20:31
    URI: https://eprints.bbk.ac.uk/id/eprint/43542

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