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Graphs and Combinatorics

, Volume 2, Issue 1, pp 113–121 | Cite as

The asymptotic number of graphs not containing a fixed subgraph and a problem for hypergraphs having no exponent

  • P. Erdös
  • P. Frankl
  • V. Rödl
Article

Abstract

LetH be a fixed graph of chromatic numberr. It is shown that the number of graphs onn vertices and not containingH as a subgraph is\(2^{(\begin{array}{*{20}c} n \\ 2 \\ \end{array} )(1 - \frac{1}{{r - 1}} + o(1))} \). Leth r (n) denote the maximum number of edges in anr-uniform hypergraph onn vertices and in which the union of any three edges has size greater than 3r − 3. It is shown thath r (n) =o(n2) although for every fixedc < 2 one has limn→∞h r (n)/n c = ∞.

Keywords

Asymptotic Number 
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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • P. Erdös
    • 1
  • P. Frankl
    • 2
  • V. Rödl
    • 3
    • 4
  1. 1.Mathematical Institute of the Hungarian Academy of ScienceBudapestHungary
  2. 2.CNRSQuai Anatole FranceParisFrance
  3. 3.Department of MathematicsFJFI, ČVUTPraha 1Czechoslovakia
  4. 4.AT&T Bell LaboratoriesMurray HillUSA

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