The study of the integrability properties of the N = 2 Landau-Ginzburg models leads naturally to a graph generalization of the Yang-Baxter equation which synthesizes the well-known vertex and RSOS Yang-Baxter equations. A non-trivial solution of this equation is found for the t2 perturbation of the A-models, which turns out to be intimately related to the Boltzmann weights of a chiral-Potts model.