A Linear Algorithm for Finding Total Colorings of Partial k-Trees

Authors:
Shuji Isobe;Xiao Zhou;Takao Nishizeki
Affiliations:
-;-;-
Venue:
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
Year:
1999

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Abstract

A total coloring of a graph G is a coloring of all elements of G, i.e. vertices and edges, in such a way that no two adjacent or incident elements receive the same color. The total coloring problem is to find a total coloring of a given graph with the minimum number of colors. Many combinatorial problems can be efficiently solved for partial k-trees, i.e., graphs with bounded tree-width. However, no efficient algorithm has been known for the total coloring problem on partial k-trees although a polynomial-time algorithm of very high order has been known. In this paper, we give a linear-time algorithm for the total coloring problem on partial k-trees with bounded.