Efficient Algorithms for Weighted Colorings of Series-Parallel Graphs

Authors:
Xiao Zhou;Takao Nishizeki
Affiliations:
-;-
Venue:
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Year:
2001

Citing 7
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Abstract

Let G be a weighted graph such that each vertex v has a positive integer weight ω(v). A weighted coloring of G is to assign a set of ω(v) colors to each vertex v so that any two adjacent vertices receive disjoint sets of colors. This paper gives an efficient algorithm to find the minimum number of colors required for a weighted coloring of a given series-parallel graph G in time O(nωmax), where n is the number of vertices and ωmax is the maximum vertex-weight of G.