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.
CITATION STYLE
Ito, T., Nishizeki, T., & Zhou, X. (2002). Algorithms for the multicolorings of partial k-trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2387, pp. 430–439). Springer Verlag. https://doi.org/10.1007/3-540-45655-4_46
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