ISSN:
1435-5914

Source:
Springer Online Journal Archives 1860-2000

Topics:
Computer Science
,
Mathematics

Notes:
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 $$\left( {\begin{array}{*{20}c} n \\ h \\ \end{array} } \right) \equiv 0(\bmod c)$$ . 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.

Type of Medium:
Electronic Resource

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