  We derive and classify all regular solutions of the boundary Yang-Baxter
equation for 19-vertex models known as Zamolodchikov-Fateev or $A_{1}^{(1)}$
model, Izergin-Korepin or $A_{2}^{(2)}$ model, sl(2|1) model and osp(2|1)
model. We find that there is a general solution for $A_{1}^{(1)}$ and sl(2|1)
models. In both models it is a complete K-matrix with three free parameters.
For the $A_{2}^{(2)}$ and osp(2|1) models we find three general solutions,
being two complete reflection K-matrices solutions and one incomplete
reflection K-matrix solution with some null entries. In both models these
solutions have two free parameters. Integrable spin-1 Hamiltonians with general
boundary interactions are also presented. Several reduced solutions from these
general solutions are presented in the appendices.
