  A graph G is perfect if for every induced subgraph H, the chromatic number of
H equals the size of the largest complete subgraph of H, and G is Berge if no
induced subgraph of G is an odd cycle of length at least 5 or the complement of
one. The "strong perfect graph conjecture" (Berge, 1961) asserts that a graph
is perfect if and only if it is Berge.
  A stronger conjecture was made recently by Conforti, Cornuejols and Vuskovic
-- that every Berge graph either falls into one of a few basic classes, or it
has a kind of separation that cannot occur in a minimal imperfect graph.
  In this paper we prove both these conjectures.
