Special Classes of Graphs
For any tree with maximum degree Δ, the equitable chromatic number is at most
with the worst case occurring for a star. However, most trees have significantly smaller equitable chromatic number: if a tree with n vertices has Δ ≤ n/3 − O(1), then it has an equitable coloring with only three colors. Furmańczyk (2006) studies the equitable chromatic number of graph products.
Read more about this topic: Equitable Coloring
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