  We develop decomposition/composition tools for efficiently solving maximum
weight stable sets problems as well as for describing them as polynomially
sized linear programs (using "compact systems"). Some of these are well-known
but need some extra work to yield polynomial "decomposition schemes".
  We apply the tools to graphs with no even hole and no cap. A hole is a
chordless cycle of length greater than three and a cap is a hole together with
an additional node that is adjacent to two adjacent nodes of the hole and that
has no other neighbors on the hole.
