For digraphs D and H, a homomorphism of D to H is a mapping f : V (D)→V (H) such that uv ∈ A(D) implies f(u)f(v) ∈ A(H). Suppose D and H are two digraphs, and ci(u), u ∈ V (D), i ∈ V (H), are nonnegative real costs. The cost of the homomorphism f of D to H is ∑ u∈V (D) cf(u)(u). The minimum cost homomorphism for a fixed digraph H, denoted by MinHOM(H), asks whether or not an input digraphD, wit...
