A directed triple system of order v with index λ, briefly by DTS（v,λ）, is a pair （X, B） where X is a v-set and B is a collection of transitive triples （blocks） on X such that every ordered pair of X belongs to λ blocks of B. A simple DTS（v, λ） is a DTS（v, λ） without repeated blocks. A simple DTS（v, ）,） is called pure and denoted by PDTS（v, λ） if （x, y, z） ∈ B implies （z, y, x）, （z, x, y）, （y, x, z）, （y, z, x）, （x, z, y） B. A large set of disjoint PDTS（v, λ）, denoted by LPDTS（v, λ）, is a collection of 3（v - 2）/λ disjoint pure directed triple systems on X. In this paper, some results about the existence for LPDTS（v, λ） are presented. Especially, we determine the spectrum of LPDTS（v, 2）.
A t-hyperwheel(t≥3) of length l(or W l(t) for brevity) is a t-uniform hypergraph(V,E) ,where E = {e1,e2,. . .,el} and v1,v2,. . .,vl are distinct vertices of V = il=1 ei such that for i = 1,. . .,l,vi,vi+1 ∈ ei and ei ∩ ej = P,j ∈/{i-1,i,i + 1},where the operation on the subscripts is modulo l and P is a vertex of V which is different from vi,1 i l. In this paper,we investigate the maximum packing problem of MPλ(3,W 4( 3) ,v) . Finally,the packing number Dλ(3,W 4( 3) ,v) is determined for any positive integers v 5 and λ.
WU Yan & CHANG YanXun Institute of Mathematics,Beijing Jiaotong University,Beijing 100044,China
Let H and J1 be both t-uniform hypergraphs. Let J2 be a sub-hypergraph of J1. In this paper, the metamorphosis of a hypergraph decomposition is introduced, denoted by (H, J1 > J2)-design, which is a generalization of the concept of metamorphosis of a graph decomposition. Let Meta(J1>J2) denote the set of all integers v such that there exists a (Kv((3)), J1>J2)-design. We completely determine the set Meta(K4((3))>K4((3))-e).
