ISSN:
1439-6912
Keywords:
05 B 30 (primary)
;
05 C 99 (secondary)
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A λ-hyperfactorization ofK 2n is a collection of 1-factors ofK 2n 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 ofK 2n with the same multiplicity γ (then λ=γ(2n−5)!!). A λ-hyperfactorization is calledsimple if each 1-factor ofK 2n 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) (i) 2n=2 a +2, λ=1 (for alla≥3); cf. Cameron [3]; (ii) 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 ofK 2n for alln≥5.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01375468
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