@Article{Furmańczyk2006,
author = "Furmańczyk, Hanna",
title = "Equitable coloring of graph products",
journal = "Opuscula Math.",
year = "2006",
volume = "26",
number = "1",
pages = "31--44",
doi = "http://dx.doi.org/10.7494/OpMath.2006.26.1.31",
url = "http://dx.doi.org/10.7494/OpMath.2006.26.1.31",
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",
issn = "1232-9274"
}