ABSTRACT
When attempting to properly color the vertices of a graphG (often with a restricted number of colors), there may be instances when (1) there is only one choice for the color of each vertex of G except for the names of the colors, (2) every vertex of G has some preassigned restriction on the choice of a color that can be used for the vertex, or (3) some vertices of G have been given preassigned colors and the remaining vertices must be colored according to these restrictions. Colorings with such restrictions are explored in this chapter.
