  A graph is prime (with respect to the split decomposition) if its vertex set
does not admit a partition (A,B) (called a split) with |A|, |B| >= 2 such that
the set of edges joining A and B induces a complete bipartite graph.
  We prove that for each n, there exists N such that every prime graph on at
least N vertices contains a vertex-minor isomorphic to either a cycle of length
n or a graph consisting of two disjoint cliques of size n joined by a matching.
