### Abstract

Let each vertex v of a graph G have a positive integer weight w(v). Then a multicoloring of G is to assign each vertex v a set of w(v) colors so that any pair of adjacent vertices receive disjoint sets of colors. A partial k-tree is a graph with tree-width bounded by a fixed constant k. This paper presents an algorithm which finds a multicoloring of any given partial k-tree G with the minimum number of colors. The computation time of the algorithm is bounded by a polynomial in the number of vertices and the maximum weight of vertices in G.

Original language | English |
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Pages (from-to) | 191-200 |

Number of pages | 10 |

Journal | IEICE Transactions on Information and Systems |

Volume | E86-D |

Issue number | 2 |

Publication status | Published - 2003 Feb |

### Keywords

- Algorithm
- Multicoloring
- Partial k-tree

### ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering
- Artificial Intelligence

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## Cite this

Ito, T., Nishizeki, T., & Zhou, X. (2003). Algorithms for multicolorings of partial k-trees.

*IEICE Transactions on Information and Systems*,*E86-D*(2), 191-200.