Exact Algorithm for Graph Homomorphism and Locally Injective Graph Homomorphism

For graphs G and H , a homomorphism from G to H is a function φ : V (G) → V (H), which maps vertices adjacent in G to adjacent vertices of H . A homomorphism is locally injective if no two vertices with a common neighbor are mapped to a single vertex in H . Many cases of graph homomorphism and locally injective graph homomorphism are NPcomplete, so there is little hope to design polynomial-time algorithms for them. In this paper we present an algorithm for graph homomorphism and locally injective homomorphism working in time O((b + 2) ), where b is the bandwidth of the complement of H .