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Algebraic Coding 1993: Algebraic Coding pp 159-163 | Cite as

Disjoint systems (Extended abstract)

  • Noga Alon
  • Benny Sudakov
Graphs and Codes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 781)

Abstract

A disjoint system of type (∀, ∃, κ, n) is a collection C={A, ..., A} of pairwise disjoint families of κ-subsets of an n-element set satisfying the following condition. For every ordered pair A i and A j of distinct members of C and for every A ε C i there exists a B ε C j that does not intersect A. Let D n (∀, ∃, κ) denote the maximum possible cardinality of a disjoint system of type (∀, ∃, κ, n). It is shown that for every fixed k≥2,
$$lim_{n \to \infty } D_n \left( {\forall ,\exists ,k} \right)\left( {\begin{array}{*{20}c}n \\k \\\end{array} } \right)^{ - 1} = \frac{1}{2}.$$

This settles a problem of Ahlswede, Cai and Zhang. Several related problems are considered as well.

Keywords

Random Graph Extremal Problem Distinct Member Probabilistic Argument Chromatic Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Noga Alon
    • 1
  • Benny Sudakov
    • 1
  1. 1.Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

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