  We describe the construction of trigonometric R-matrices corresponding to the
(multiplicity-free) tensor product of any two irreducible representations of a
quantum algebra $U_q(\G)$. Our method is a generalization of the tensor product
graph method to the case of two different representations. It yields the
decomposition of the R-matrix into projection operators. Many new examples of
trigonometric R-matrices (solutions to the spectral parameter dependent
Yang-Baxter equation) are constructed using this approach.
