Hexagon quadrangle systems

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-fo...

Perfect dodecagon quadrangle systems

A dodecagon quadrangle is the graph consisting of two cycles: a 12-cycle (x1, x2, ..., x12) and a 4-cycle (x1, x4, x7, x10). A dodecagon quadrangle system of order n and index ρ [DQS] is a pair (X, H), where X is a finite set of n vertices and H is a collection of edge disjoint dodecagon quadrangles (called blocks) which partitions the edge set of ρKn, with vertex set X. A dodecagon quadrangle ...

Hexagon biquadrangle systems

A small embedding for partial hexagon systems

Although these necessary conditions are sufficient for all n ::; 50 [3], as well as several infinite classes [1, 4, 5, 7, 8, 11], the existence problem is far from settled in general. This will be of no consequence here since we will be considering 6-cycle systems only. It is a well-known Folk Theorem that the spectrum for 6-cycle systems (i.e, the set of all n such that a 6-cycle system of ord...

Embedding Steiner triple systems in hexagon triple systems