We start by proving that the Henson graphs , (the homogeneous countable graphs universal for the class of all finite graphs omitting the clique of size ), are retract rigid. On the other hand, we provide a full characterization of retracts of the complement of . Further, we prove that each countable partial order embeds in the natural order of retractions of the complements of Henson graphs. Finally, we show that graphs omitting sufficiently large null subgraphs omit certain configurations in their endomorphism monoids.
