New Results on Generalized Graph Coloring
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 V 1,...,V k so that V j induces a graph in the class ℘ j (j=1,2,...,k). If ℘ 1 =...=℘ k is the class of edgeless graphs, the...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2004-12-01
|
| Series: | Discrete Mathematics & Theoretical Computer Science |
| Online Access: | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/187 |
| Summary: | 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 V 1,...,V k so that V j 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. |
|---|---|
| ISSN: | 1462-7264 1365-8050 |