Graph Theory and Probability

  • P. Erdös
Part of the Modern Birkhäuser Classics book series (MBC)


A well-known theorem of Ramsay (8; 9) states that to every n there exists a smallest integer g(n) so that every graph of g(n) vertices contains either a set of n independent points or a complete graph of order n, but there exists a graph of g(n) – 1 vertices which does not contain a complete subgraph of n vertices and also does not contain a set of n independent points. (A graph is called complete if every two of its vertices are connected by an edge; a set of points is called independent if no two of its points are connected by an edge.)


Complete Graph Chromatic Number Explicit Construction Closed Circuit Complete Subgraph 
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Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • P. Erdös
    • 1
  1. 1.University of Toronto and TechnionHaifaIsrael

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