Résumé
In this article, given two finite simplicial graphs Gamma(1) and Gamma(2), we state and prove a complete description of the possible morphisms C(Gamma(1)) -> C(Gamma(2)) between the right-angled Coxeter groups C(Gamma(1)) and C(Gamma(2)). As an application, assuming that Gamma(2) is triangle-free, we show that, if C(Gamma(1)) is isomorphic to a subgroup of C(Gamma(2)), then the ball of radius 8 vertical bar Gamma(1)vertical bar vertical bar Gamma(2)vertical bar in C(Gamma(2)) contains the basis of a subgroup isomorphic to C(Gamma(1)). This provides an algorithm determining whether or not, among two given two-dimensional right-angled Coxeter groups, one is isomorphic to a subgroup of the other.