Opuscula Math. 26, no. 1 (2006), 31-44

Opuscula Mathematica

Equitable coloring of graph products

Hanna Furmańczyk

Abstract. A graph is equitably \(k\)-colorable if its vertices can be partitioned into \(k\) independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest \(k\) for which such a coloring exists is known as the equitable chromatic number of \(G\) and denoted by \(\chi_{=}(G)\). It is interesting to note that if a graph \(G\) is equitably \(k\)-colorable, it does not imply that it is equitably \((k+1)\)-colorable. The smallest integer \(k\) for which \(G\) is equitably \(k'\)-colorable for all \(k'\geq k\) is called the equitable chromatic threshold of \(G\) and denoted by \(\chi_{=}^{*}(G)\). In the paper we establish the equitable chromatic number and the equitable chromatic threshold for certain products of some highly-structured graphs. We extend the results from [Chen B.-L., Lih K.-W., Yan J.-H., Equitable coloring of graph products, manuscript, 1998] for Cartesian, weak and strong tensor products.

Keywords: equitable coloring, graph product.

Mathematics Subject Classification: 05C15, 68R10.

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  • Hanna Furmańczyk
  • Gdańsk University, Mathematical Institute, Wita Stwosza 57, 80-952 Gdańsk, Poland
  • Received: 2005-04-28.
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Hanna Furmańczyk, Equitable coloring of graph products, Opuscula Math. 26, no. 1 (2006), 31-44

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