In graph theory, an acyclic coloring is a (proper) vertex coloring in which every 2-chromatic subgraph is acyclic.The acyclic chromatic number A(G) of a graph G is the least number of colors needed in any acyclic coloring of G. In graph theory, an acyclic coloring is a (proper) vertex coloring in which every 2-chromatic subgraph is acyclic.The acyclic chromatic number A(G) of a graph G is the least number of colors needed in any acyclic coloring of G.