Let I 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 an
y two vertices u and v get different colors if the distance between u and v
in G is at most I. In this paper we give an algorithm to find an l-colorin
g 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 I and k are bounded inte
gers.