in graph theory, a t-coloring of a graph formula_1, given the set "t" of nonnegative integers containing 0, is a function formula_2 that maps each vertex of g to a positive integer (color) such that formula_3. in simple words, the absolute value of the difference between two colors of adjacent vertices must not belong to fixed set "t". the concept was introduced by william k. hale. if "t = {0}" it reduces to common vertex coloring.