Hoede-sequences

F. Gobel

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    Abstract

    In an attempt to prove the double-cycle-conjecture for cubic graphs, C. Hoede formulated the following combinatorial problem. “Given a partition of {1, 2, . . . , 3n} into n equal classes, is it possible to choose from each class a number such that these numbers form an increasing sequence of alternating parity?��? Let a Hoede-sequence be defined as an increasing sequence of natural numbers of alternating parity. We determine the average number of Hoede-sequences w.r.t. arbitrary partitions, and obtain bounds for the maximum and minimum number of Hoede-sequences w.r.t. partitions into equal classes.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Publication statusPublished - 2001

    Publication series

    NameMemorandum
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1591
    ISSN (Print)0169-2690

    Keywords

    • EWI-3411
    • IR-65778
    • MSC-05A15
    • MSC-05A16
    • MSC-05A18

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