linguistic:translation, structural:reformatting
Variants

General homomorphisms can also be thought of as a kind of coloring: if the vertices of a fixed graph H are the available colors and edges of H describe which colors are compatible, then an H -coloring of G is an assignment of colors to vertices of G such that adjacent vertices get compatible colors.Many notions of graph coloring fit into this pattern and can be expressed as graph homomorphisms into different families of graphs. Circular colorings can be defined using homomorphisms into circular complete graphs, refining the usual notion of colorings. Fractional and b -fold coloring can be defined using homomorphisms into Kneser graphs. T-colorings correspond to homomorphisms into certain infinite graphs. An oriented coloring of a directed graph is a homomorphism into any oriented graph. An L(2,1)-coloring is a homomorphism into the complement of the path graph that is locally injective, meaning it is required to be injective on the neighbourhood of every vertex.