Asymptotically good coverings

Research output: Contribution to journalArticle

Abstract

The Erdos-Hanani conjecture is that for fixed r <k and n large there exists a covering of all r-sets of an n-set by a family of k-sets whose cardinality is asymptotic (in n) to the "counting" lower bound. This conjecture was first proven by Rodl, here we give a more direct argument. We use probabilistic methods, selecting k-sets in large groups, and showing that the hypergraph of uncovered r-sets retains a property we call quasirandomness, meaning that it has the essential (for us) properties of random hypergraph.

Original languageEnglish (US)
Pages (from-to)575-586
Number of pages12
JournalPacific Journal of Mathematics
Volume118
Issue number2
StatePublished - 1985

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Covering
Hypergraph
Probabilistic Methods
Erdös
Cardinality
Counting
Lower bound

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Asymptotically good coverings. / Spencer, Joel.

In: Pacific Journal of Mathematics, Vol. 118, No. 2, 1985, p. 575-586.

Research output: Contribution to journalArticle

Spencer, Joel. / Asymptotically good coverings. In: Pacific Journal of Mathematics. 1985 ; Vol. 118, No. 2. pp. 575-586.
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