Abstract
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.
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Ito, T., Nishizeki, T., Zhou, X. (2002). Algorithms for the Multicolorings of Partial k-Trees. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_46
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DOI: https://doi.org/10.1007/3-540-45655-4_46
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