A Cyclic Coloring Of Graphs Of Maximum Degree △≥5

In this paper, we introduce the development of acyclic coloring of graphand the study current status of it, and show that any graph with maximumdegree△≥5 has acyclic chromatic number at most a(G)≤[(△-1)~2/2] , andwe give a greedy algorithm that achieves this bound. This result is less thanthe best general upper bound a(G)≤△(△-1)/2. And draw two new resultsas follows: a(G)≤8, if any graph of△= 5; a(G)≤12, if any graph of△= 6.