# IJPAM: Volume 71, No. 2 (2011)

**ON EQUITABLE COLORING OF**

COMPLETE -PARTITE GRAPHS

COMPLETE -PARTITE GRAPHS

Applied Mathematics Research Group

Faculty of Science

Khon Kaen University

40002, THAILAND

**Abstract. **Let denote the equitable chromatic number of a graph and let
denote a complete -partite graph with
Note that
In this paper, we investigate the neccessary conditions on the number of vertices such that this bound is attained. By using those conditions, we obtain the algorithm to find the equitable chromatic number of a complete -partite graph
with complexity

Moreover for a complete bipartite graph and a given integer we find the minimum integer such that for every integer implies
For a complete -partite graph
with
and a given integer we find the minimum integer such that for every integer
implies

**Received: **May 4, 2011

**AMS Subject Classification: **05C15, 05C35

**Key Words and Phrases: **equitable coloring, complete -partite graph, algorithm

**Download paper from here.**

**Source:**International Journal of Pure and Applied Mathematics

**ISSN printed version:**1311-8080

**ISSN on-line version:**1314-3395

**Year:**2011

**Volume:**71

**Issue:**2