### Abstract

We investigate a restricted list-coloring problem. Given a graph G = (V,E), a non empty set of colors L, and a nonempty subset L(v) of L for each vertex v, find an L-coloring of G with the size of each class of colors being equal to a given integer. This restricted list-coloring problem was proposed by de Werra. We prove that this problem is script N sign P-Complete even if the graph is a path with at most two colors on each vertex list. We then give a polynomial algorithm which solves this problem for the case where the total number of colors occurring in all lists is fixed.

Original language | English (US) |
---|---|

Pages (from-to) | 103-109 |

Number of pages | 7 |

Journal | Discrete Mathematics |

Volume | 195 |

Issue number | 1-3 |

State | Published - 1999 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*195*(1-3), 103-109.

**On the complexity of a restricted list-coloring problem.** / Dror, Moshe; Finke, Gerd; Gravier, Sylvain; Kubiak, Wieslaw.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 195, no. 1-3, pp. 103-109.

}

TY - JOUR

T1 - On the complexity of a restricted list-coloring problem

AU - Dror, Moshe

AU - Finke, Gerd

AU - Gravier, Sylvain

AU - Kubiak, Wieslaw

PY - 1999

Y1 - 1999

N2 - We investigate a restricted list-coloring problem. Given a graph G = (V,E), a non empty set of colors L, and a nonempty subset L(v) of L for each vertex v, find an L-coloring of G with the size of each class of colors being equal to a given integer. This restricted list-coloring problem was proposed by de Werra. We prove that this problem is script N sign P-Complete even if the graph is a path with at most two colors on each vertex list. We then give a polynomial algorithm which solves this problem for the case where the total number of colors occurring in all lists is fixed.

AB - We investigate a restricted list-coloring problem. Given a graph G = (V,E), a non empty set of colors L, and a nonempty subset L(v) of L for each vertex v, find an L-coloring of G with the size of each class of colors being equal to a given integer. This restricted list-coloring problem was proposed by de Werra. We prove that this problem is script N sign P-Complete even if the graph is a path with at most two colors on each vertex list. We then give a polynomial algorithm which solves this problem for the case where the total number of colors occurring in all lists is fixed.

UR - http://www.scopus.com/inward/record.url?scp=0347366240&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347366240&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0347366240

VL - 195

SP - 103

EP - 109

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -