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The Equitable Coloring of Graphs

In: Handbook of Combinatorial Optimization

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  • Ko-Wei Lih

    (Academia Sinica, Institute of Mathematics)

Abstract

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.

Suggested Citation

  • Ko-Wei Lih, 1998. "The Equitable Coloring of Graphs," Springer Books, in: Ding-Zhu Du & Panos M. Pardalos (ed.), Handbook of Combinatorial Optimization, pages 2015-2038, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0303-9_31
    DOI: 10.1007/978-1-4613-0303-9_31
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