Abstract: A graph is equitably k-colorable if its vertices can be partitioned into k inde- pendent sets of as near equal sizes as possible.In this paper,we determine a suficient and necessary condition for which a complete r-parite graph is equitably k-colorable.From this result,we can provide another way to prove some previous results.

Key words: complete r-partite graph, equitably k-colorable, equitable chromatic number