# 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 ℘, Generalized Graph Coloring is the problem of deciding whether the vertex set of a given
graph _{1},...,℘_{k}G can be partitioned into subsets
V so that _{1},...,V_{k}V induces a graph
in the class _{j}℘ _{j}(j=1,2,...,k). If
℘ is the class of edgeless
graphs, then this problem coincides with
the standard vertex _{1}=...=℘_{k}k-COLORABILITY,
which is known to be NP-complete for any k≥ 3.
Recently, this result has been generalized by
showing that if all ℘'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.
_{i}If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |

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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Automatically produced on Sat Jun 19 16:17:52 CEST 2004 by gustedt