Packing,covering and decomposing of a complete uniform hypergraph into delta-systems |
| |
Authors: | Zbigniew Lonc |
| |
Institution: | (1) Institute of Mathematics, Warsaw University of Technology, Warsaw, Poland |
| |
Abstract: | Anh-uniform hypergraph generated by a set of edges {E
1,...,E
c} is said to be a delta-system Δ(p,h,c) if there is ap-element setF such that ∇F|=p andE
i⌢E
j=F,∀i≠j.
The main result of this paper says that givenp, h andc, there isn
0 such that forn≥n
0 the set of edges of a completeh-uniform hypergraphK
n
h can be partitioned into subsets generating isomorphic delta-systems Δ(p, h, c) if and only if
. This result is derived from a more general theorem in which the maximum number of delta-systems Δ(p, h, c) that can be packed intoK
n
h and the minimum number of delta-systems Δ(p, h, c) that can cover the edges ofK
n
h are determined for largen. Moreover, we prove a theorem on partitioning of the edge set ofK
n
h into subsets generating small but not necessarily isomorphic delta-systems. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|