We consider homomorphisms of signed graphs from a computational perspective. In particular, we study the list homomorphism problem seeking an input graph $(G,\sigma)$, equipped with lists $L(v) \subseteq V(H), v \in V(G)$, allowed images, to fixed target $(H,\pi)$. The complexity similar without (corresponding all being $L(v)=V(H)$) has been previously classified by Brewster and Siggers, but ve...

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...

A homomorphism from a graph G to a graph H is a function from the vertices of G to the vertices of H that preserves edges. A homomorphism is surjective if it uses all of the vertices of H and it is a compaction if it uses all of the vertices of H and all of the non-loop edges of H . Hell and Nešetřil gave a complete characterisation of the complexity of deciding whether there is a homomorphism ...

A. M. S. Classification: 18G30, 18G55.

It is known that a countable ω-categorical structure interprets all finite structures primitively positively if and only if its polymorphism clone maps to the clone of projections on a two-element set via a continuous clone homomorphism. We investigate the relationship between the existence of a clone homomorphism to the projection clone, and the existence of such a homomorphism which is contin...