  We show that graphs that do not contain a theta, pyramid, prism, or turtle as
an induced subgraph have polynomially many minimal separators. This result is
the best possible in the sense that there are graphs with exponentially many
minimal separators if only three of the four induced subgraphs are excluded. As
a consequence, there is a polynomial time algorithm to solve the maximum weight
independent set problem for the class of (theta, pyramid, prism, turtle)-free
graphs. Since every prism, theta, and turtle contains an even hole, this also
implies a polynomial time algorithm to solve the maximum weight independent set
problem for the class of (pyramid, even hole)-free graphs.
