Abstract：An acyclic coloring of a graph is a proper vertex coloring and no bichromatic cycles. In order to study the acyclic coloring of graphs with maximum degree of 5. classified coloring, exhaustion coloring and the color-changing technique of structure of graphs were discussed. The results proved that when graph of maximum degree is 5, its acyclic chromatic number is less than 7.

Keyword：acyclic coloring;acyclic chromatic number;maximum degree;