A criterion of containment for tropical hypersurfaces

For tropical n-variable polynomials f, g a criterion of containment for tropical hypersurfaces Trop(f)⊂ Trop(g) is provided in terms of their Newton polyhedra N(f), N(g)⊂ℝ^n+1. Namely, Trop(f)⊂ Trop(g) iff for every vertex v of N(g) there exist a homothety t· N(f), t>0 and a parallel shift s:ℝ^n+1→ℝ^n+1 such that v∈ s(t· N(f))⊂ N(g).