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Volume :14 Issue : 2 1987      Add To Cart                                                                    Download

Hyperfactorizations of graphs and 5-designs

Auther : DIETER JUNGNICKEL AND SCOTT A. VANSTONE

Mathematisches Institut, Justus-Liebig-Universitat Giessen, Arndtstr 2, D-6300 Giessen, Federal Republic of Germany, adn Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3GL
 

ABSTRACT

 

A hyperfactorization of index g, of thecomplete graph K2n is a collection H of 1-factors such that each pair of disjoint edges occurs in precisely g factors in H. Generalizing a result of Lonz and Vanstone, we show that each such hyperfactorization may be used to construct a 5-design S15g (5,6,2n); if n is divisible by 3, this 5-deslgn will be resolvable. We study the 5-designs belonging to hyperfactorizations of index 1 constructed from a regular hyperoval in PG(2,2a) and investigate the structure of repeated blocks in these examples. Except for a = 2 or 3, none of these designs is simple, but all are irreducible. 15-fold blocks will occur if and only if a is even. We also give two examples of nontrivial hyperfactorizations of index  g ¹1, associated with the Mathieu groups M12, and M24

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