  The relational complexity, introduced by G. Cherlin, G. Martin, and D.
Saracino, is a measure of ultrahomogeneity of a relational structure. It
provides an information on minimal arity of additional invariant relations
needed to turn given structure into an ultrahomogeneous one. The original
motivation was group theory. This work focuses more on structures and provides
an alternative approach. Our study is motivated by related concept of lift
complexity studied by Hubicka and Nesetril.
