Hoede-sequences

F. Gobel

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 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

Access to Document

1591
open
1591
open

Cite this

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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.",

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series = "Memorandum",

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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.

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KW - IR-65778

KW - MSC-05A15

KW - MSC-05A16

KW - MSC-05A18

M3 - Report

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BT - Hoede-sequences

PB - University of Twente, Department of Applied Mathematics

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