The existence of non-trivial hyperfactorizations ofK2n View Full Text


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Article Info

DATE

1991-03

AUTHORS

Endre Boros, Dieter Jungnickel, Scott A. Vanstone

ABSTRACT

A λ-hyperfactorization ofK2n is a collection of 1-factors ofK2n for which each pair of disjoint edges appears in precisely λ of the 1-factors. We call a λ-hyperfactorizationtrivial if it contains each 1-factor ofK2n with the same multiplicity γ (then λ=γ(2n−5)!!). A λ-hyperfactorization is calledsimple if each 1-factor ofK2n appears at most once. Prior to this paper, the only known non-trivial λ-hyperfactorizations had one of the following parameters (or were multipliers of such an example)2n=2a+2, λ=1 (for alla≥3); cf. Cameron [3];2n=12, λ=15 or 2n=24, λ=495; cf. Jungnickel and Vanstone [8].In the present paper we show the existence of non-trivial simple λ-hyperfactorizations ofK2n for alln≥5. More... »

PAGES

9-15

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Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01375468

DOI

http://dx.doi.org/10.1007/bf01375468

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1047108867


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