The Mathematics of Paul Erdös II pp 70-78

Part of the Algorithms and Combinatorics book series (AC, volume 14)

Hereditary and Monotone Properties of Graphs

  • Béla Bollobás
  • Andrew Thomason

Summary

Given a hereditary graph property Ρ let Ρn be the set of those graphs in Ρ on the vertex set {1, …, n}. Define the constant cn by \(\left| {P^n } \right| = 2^{cn(_2^n )} .\) We show that the limit limn → ∞ cn always exists and equals 1 − 1/r, where r is a positive integer which can be described explicitly in terms of Ρ. This result, obtained independently by Alekseev, extends considerably one of Erdős, Frankl and Rödl concerning principal monotone properties and one of Prömel and Steger concerning principal hereditary properties.

AMS Subject Classification: Primary 05C35, Secondary 05C30.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Béla Bollobás
    • 1
  • Andrew Thomason
    • 1
  1. 1.Department of Pure Mathematics and Mathematical StatisticsCambridgeEngland

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