### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 2001 |

### Publication series

Name | Memorandum |
---|---|

Publisher | Department 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

*Hoede-sequences*. (Memorandum; No. 1591). Enschede: University of Twente, Department of Applied Mathematics.

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*Hoede-sequences*. Memorandum, no. 1591, University of Twente, Department of Applied Mathematics, Enschede.

**Hoede-sequences.** / Gobel, F.

Research output: Book/Report › Report › Other 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 -