Discrete Mathematics & Theoretical Computer Science


Volume 6 n° 2 (2004), pp. 215-222

author:Vladimir E. Alekseev and Alastair Farrugia and Vadim V. Lozin
title:New Results on Generalized Graph Coloring
keywords:Generalized Graph Coloring; Polynomial algorithm; NP-completeness
abstract:For graph classes 1,...,℘k, Generalized Graph Coloring is the problem of deciding whether the vertex set of a given graph G can be partitioned into subsets V1,...,Vk so that Vj induces a graph in the class j (j=1,2,...,k). If 1=...=℘k is the class of edgeless graphs, then this problem coincides with the standard vertex k-COLORABILITY, which is known to be NP-complete for any k≥ 3. Recently, this result has been generalized by showing that if all i's are additive hereditary, then the generalized graph coloring is NP-hard, with the only exception of bipartite graphs. Clearly, a similar result follows when all the i's are co-additive.

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reference: Vladimir E. Alekseev and Alastair Farrugia and Vadim V. Lozin (2004), New Results on Generalized Graph Coloring, Discrete Mathematics and Theoretical Computer Science 6, pp. 215-222
bibtex:For a corresponding BibTeX entry, please consider our BibTeX-file.
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