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. A graph G is s-degenerated for a positive integer s if G can be reduced to a trivial graph by successive removal of vertices with degree ≤ s. We prove that an s-degenerated graph G has a total coloring with δ + 1 colors if the maximum degree δ of G is su-ciently large, say δ ≥ 4s+3. Our proof yields an eficient algorithm to find such a total coloring. We also give a linear-time algorithm to find a total coloring of a graph G with the minimum number of colors if G is a partial k-tree, i.e. the tree-width of G is bounded by a fixed integer k. © 2011 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Isobe, S., Zhou, X., & Nishizeki, T. (2001). Total colorings of degenerated graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2076 LNCS, pp. 506–517). Springer Verlag. https://doi.org/10.1007/3-540-48224-5_42
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