The Equitable Coloring of Graphs
Let the vertices of a graph G be colored with k colors such that no adjacent vertices receive the same color and the sizes of the color classes differ by at most one. Then G is said to be equitably k-colorable. The equitable chromatic number x = (G) is the smallest integer k such that G is equitably k-colorable. In this article, we survey recent progress on the equitable coloring of graphs. We pay more attention to work done on the Equitable ∆-Coloring Conjecture. We also discuss related graph coloring notions and their problems. The survey ends with suggestions for further research topics.
KeywordsEquitable coloring Equitable edge coloring m-bounded coloring Equalized total coloring
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