Journalartikel

Jahr der Veröffentlichung: 1991

Seiten: 9-15

Zeitschrift: Combinatorica

Bandnummer: 11

Heftnummer: 1

ISSN: 0209-9683

DOI Link: https://doi.org/10.1007/BF01375468

Verlag: Springer

Abstract: 

A lambda-hyperfactorization of K2n is a collection of 1-factors of K2n for which each pair of disjoint edges appears in precisely-lambda of the 1-factors. We call a lambda-hyperfactorization trivial if it contains each 1-factor of K2n with the same multiplicity-gamma (then lambda = gamma(2n - 5)!!). A lambda-hyperfactorization is called simple if each 1-factor of K2n appears at most once. Prior to this paper, the only known non-trivial lambda-hyperfactorizations had one of the following parameters (or were multipliers of such an example) (i) 2n = 2a + 2, lambda = 1 (for all a greater-than-or-equal-to 3); cf. Cameron [3]; (ii) 2n = 12, lambda = 15 or 2n = 24, lambda = 495; cf. Jungnickel and Vanstone [8].

In the present paper we show the existence of non-trivial simple lambda-hyperfactorizations of K2n for all n greater-than-or-equal-to 5.

Harvard-Zitierstil: BOROS, E., JUNGNICKEL, D. and VANSTONE, S. (1991) THE EXISTENCE OF NONTRIVIAL HYPERFACTORIZATIONS OF K2N, Combinatorica, 11(1), pp. 9-15. https://doi.org/10.1007/BF01375468

APA-Zitierstil: BOROS, E., JUNGNICKEL, D., & VANSTONE, S. (1991). THE EXISTENCE OF NONTRIVIAL HYPERFACTORIZATIONS OF K2N. Combinatorica. 11(1), 9-15. https://doi.org/10.1007/BF01375468