Hexagon quadrangle systems

A hexagon quadrangle system of order n and index [HQS (n)] is a pair (X,H), where X is a finite set of n vertices and H is a collection of edge disjoint hexagon quadrangles (called blocks) which partitions the edge set of Kn, with vertex set X. A hexagon quadrangle system is said to be a 4-nesting [N(4) − HQS] if the collection of all the 4-cycles contained in the hexagon quadrangles is a /2-fold 4-cycle system. It is said to be a 6-nesting [N(6) − HQS] if the collection of 6-cycles contained in the hexagon quadrangles is a ( 3 4 )-fold 6-cycle system. It is said to be a (4, 6)-nesting, briefly a N(4, 6)−HQS, if it is both a 4-nesting and a 6-nesting. In this paper we determine completely the spectrum of N(4, 6)− HQS for = 6h, = 4h and = 8h, h positive integer. © 2007 Elsevier B.V. All rights reserved.