A Note on Triangle-Free Graphs

  • Paul Erdős
  • Svante Janson
  • Tomasz Łuczak
  • Joel Spencer
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 76)

Abstract

There is a natural, if imprecise, notion that the requirement of trianglefreeness on a graph G forces it into a bipartite-like form. In an extreme case, if G has n vertices and edges then Turán’s Theorem gives that it must be the bipartite graph Our concern here is what happens when e is smaller, must G still exhibit bipartite-like behavior. Very roughly, our answer is: Yes, if en 3/2, No otherwise.

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References

  1. [1]
    P. Erdős, Graph Theory and Probability II, Canad. J. Math 13 (1961), 346–352.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Paul Erdős
    • 1
  • Svante Janson
    • 2
  • Tomasz Łuczak
    • 3
  • Joel Spencer
    • 4
  1. 1.Mathematics InstituteBudapestHungary
  2. 2.Department of MathematicsUppsala UniversityUppsalaSweden
  3. 3.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  4. 4.Department of Computer ScienceCourant Institute, New York UniversityNew YorkUSA

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