In graph theory, Brooks' theorem states a relationship between the maximum degree of a graph and its chromatic number. According to the theorem, in a connected graph in which every vertex has at most Δ neighbors, the vertices can be colored with only Δ colors, except for two cases, complete graphs and cycle graphs of odd length, which require Δ + 1 colors.
The theorem is named after R. Leonard Brooks, who published a proof of it in 1941.[1] A coloring with the number of colors described by Brooks' theorem is sometimes called a Brooks coloring[2] or a Δ-coloring.[3]