The greedy algorithm considers the vertices in a specific order formula_73,…,formula_74 and assigns to formula_75 the smallest available color not used by formula_75’s neighbours among formula_73,…,formula_78, adding a fresh color if needed. The quality of the resulting coloring depends on the chosen ordering. There exists an ordering that leads to a greedy coloring with the optimal number of formula_79 colors. On the other hand, greedy colorings can be arbitrarily bad; for example, the crown graph on "n" vertices can be 2-colored, but has an ordering that leads to a greedy coloring with formula_80 colors.