Trivially, the maximum chromatic number of a graph on n vertices is n, and the only graph which achieves this value is the complete graph  K__n.  It is natural to ask whether this result is "stable", i.e.,  if n  is large, G  has n vertices and the chromatic number of G is close to n, must G  be close to being a complete graph? It is easy to see that for each  c>0, if  G  has n  vertices and chromatic number at least  n−c, then it contains a clique whose size is at least  n−2c.

We will consider the analogous questions for posets and dimension.  Now the discussion will really become interesting.