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...

A graph homomorphism is an edge preserving vertex mapping between two graphs. Locally constrained homomorphisms are those that behave well on the neighborhoods of vertices — if the neighborhood of any vertex of the source graph is mapped bijectively (injectively, surjectively) to the neighborhood of its image in the target graph, the homomorphism is called locally bijective (injective, surjecti...

In this paper, we define some new homomorphism-monotone parameters for hypergraphs. Using these parameters, we extend some graph homomorphism results to hypergraph case. Also, we present some bounds for some well-known invariants of hypergraphs such as fractional chromatic number,independent numer and some other invariants of hyergraphs, in terms of these parameters.