### 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 language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 2001 |

### Publication series

Name | Memorandum |
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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

Gobel, F. (2001).

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