@inproceedings{Aramayona2013FINITERS,
title={FINITE RIGID SETS IN CURVE COMPLEXES},
author={Javier Aramayona and Christopher J. Leininger},
year={2013}
}

We prove that curve complexes of surfaces are finitely rigid: for every orientable surface S of finite topological type, we identify a finite subcomplex X of the curve complex C(S) such that every locally injective simplicial map X → C(S) is the restriction of an element of Aut(C(S)), unique up to the (finite) point-wise stabilizer of X in Aut(C(S)). Furthermore, if S is not a twice-punctured torus, then we can replace Aut(C(S)) in this statement with the extended mapping class group Mod±(S).