Hoede-sequences

F. Gobel

    Research output: Book/ReportReportOther research output

    72 Downloads (Pure)

    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

    Cite this

    Gobel, F. (2001). Hoede-sequences. (Memorandum; No. 1591). Enschede: University of Twente, Department of Applied Mathematics.
    Gobel, F. / Hoede-sequences. Enschede : University of Twente, Department of Applied Mathematics, 2001. (Memorandum; 1591).
    @book{46b3630ac74f4845aa86f61fd18f49d3,
    title = "Hoede-sequences",
    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.",
    keywords = "EWI-3411, IR-65778, MSC-05A15, MSC-05A16, MSC-05A18",
    author = "F. Gobel",
    note = "Imported from MEMORANDA",
    year = "2001",
    language = "Undefined",
    series = "Memorandum",
    publisher = "University of Twente, Department of Applied Mathematics",
    number = "1591",

    }

    Gobel, F 2001, Hoede-sequences. Memorandum, no. 1591, University of Twente, Department of Applied Mathematics, Enschede.

    Hoede-sequences. / Gobel, F.

    Enschede : University of Twente, Department of Applied Mathematics, 2001. (Memorandum; No. 1591).

    Research output: Book/ReportReportOther research output

    TY - BOOK

    T1 - Hoede-sequences

    AU - Gobel, F.

    N1 - Imported from MEMORANDA

    PY - 2001

    Y1 - 2001

    N2 - 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.

    AB - 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.

    KW - EWI-3411

    KW - IR-65778

    KW - MSC-05A15

    KW - MSC-05A16

    KW - MSC-05A18

    M3 - Report

    T3 - Memorandum

    BT - Hoede-sequences

    PB - University of Twente, Department of Applied Mathematics

    CY - Enschede

    ER -

    Gobel F. Hoede-sequences. Enschede: University of Twente, Department of Applied Mathematics, 2001. (Memorandum; 1591).