  For $n\geq 3$, let $(H_n, E)$ denote the $n$-th Henson graph, i.e., the
unique countable homogeneous graph with exactly those finite graphs as induced
subgraphs that do not embed the complete graph on $n$ vertices. We show that
for all structures $\Gamma$ with domain $H_n$ whose relations are first-order
definable in $(H_n,E)$ the constraint satisfaction problem for $\Gamma$ is
either in P or is NP-complete.
  We moreover show a similar complexity dichotomy for all structures whose
relations are first-order definable in a homogeneous graph whose reflexive
closure is an equivalence relation.
  Together with earlier results, in particular for the random graph, this
completes the complexity classification of constraint satisfaction problems of
structures first-order definable in countably infinite homogeneous graphs: all
such problems are either in P or NP-complete.
