Norm-Graphs: Variations and Applications

Noga Alon, L. Rónyai, Tibor Szabó

Research output: Contribution to journalArticle

76 Citations (Scopus)

Abstract

We describe several variants of the norm-graphs introduced by Kollár, Rónyai, and Szabó and study some of their extremal properties. Using these variants we construct, for infinitely many values of n, a graph on n vertices with more than 12n5/3 edges, containing no copy of K3, 3, thus slightly improving an old construction of Brown. We also prove that the maximum number of vertices in a complete graph whose edges can be colored by k colors with no monochromatic copy of K3, 3 is (1+o(1))k3. This answers a question of Chung and Graham. In addition we prove that for every fixed t, there is a family of subsets of an n element set whose so-called dual shatter function is O(mt) and whose discrepancy is Ω(n1/2-1/2tlogn). This settles a problem of Matoušek.

Original languageEnglish
Pages (from-to)280-290
Number of pages11
JournalJournal of Combinatorial Theory. Series B
Volume76
Issue number2
DOIs
Publication statusPublished - Jul 1999

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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Norm-Graphs : Variations and Applications. / Alon, Noga; Rónyai, L.; Szabó, Tibor.

In: Journal of Combinatorial Theory. Series B, Vol. 76, No. 2, 07.1999, p. 280-290.

Research output: Contribution to journalArticle

Alon, Noga ; Rónyai, L. ; Szabó, Tibor. / Norm-Graphs : Variations and Applications. In: Journal of Combinatorial Theory. Series B. 1999 ; Vol. 76, No. 2. pp. 280-290.
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