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Hoede-sequences

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Göbel, F. (2001) Hoede-sequences. [Report]

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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?U+00e2U+0080?
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.
Item Type:Report
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
Link to this item:http://purl.utwente.nl/publications/65778
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