Algorithms for Multicolorings of Partial k-Trees

Takehiro ITO  Takao NISHIZEKI  Xiao ZHOU  

IEICE TRANSACTIONS on Information and Systems   Vol.E86-D   No.2   pp.191-200
Publication Date: 2003/02/01
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Issue on Selected Papers from LA Symposium)
Category: Graph Algorithms
algorithm,  multicoloring,  partial k-tree,  

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Let each vertex v of a graph G have a positive integer weight ω(v). Then a multicoloring of G is to assign each vertex v a set of ω(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.