Greedy F-colorings of graphs Original Research Article

Let G=(V,E) be a connected graph. For a symmetric, integer-valued function δ on V×V, where K is an integer constant, N0 is the set of nonnegative integers, and Z is the set of integers, we define a C-mapping F : V×V×N0→Z by F(u,v,m)=δ(u,v)+m−K. A coloring c of G is an F-coloring if F(u,v,|c(u)−c(v)|)⩾0 for every two distinct vertices u and v of G. The maximum color assigned by c to a vertex of G is the value of c, and the F-chromatic number F(G) is the minimum value among all F-colorings of G. For an ordering s: v1,v2,…,vn of the vertices of G, a greedy F-coloring c of s is defined by (1) c(v1)=1 and (2) for each i with 1⩽i