Graph Theory and Probability
P. Erdös · Birkhäuser Boston eBooks · 2009
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.) 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.