Generalized Vertex-Colorings of Partial k-Trees

Xiao ZHOU  Yasuaki KANARI  Takao NISHIZEKI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.4   pp.671-678
Publication Date: 2000/04/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
algorithm,  generalized vertex-coloring,  l-coloring,  partial k-tree,  

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Let l be a positive integer, and let G be a graph with nonnegative integer weights on edges. Then a generalized vertex-coloring, called an l-coloring of G, is an assignment of colors to the vertices of G in such a way that any two vertices u and v get different colors if the distance between u and v in G is at most l. In this paper we give an algorithm to find an l-coloring of a given graph G with the minimum number of colors. The algorithm takes polynomial time if G is a partial k-tree and both l and k are bounded integers.