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Graph Theory and Probability

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

Abstract

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.)

Keywords

Complete Graph Chromatic Number Explicit Construction Closed Circuit Complete Subgraph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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