@inproceedings{c5934f23f619499b96405d1777d18ea5,

title = "Total colorings of degenerated graphs",

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. 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.",

author = "Shuji Isobe and Xiao Zhou and Takao Nishizeki",

year = "2001",

doi = "10.1007/3-540-48224-5_42",

language = "English",

isbn = "3540422870",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "506--517",

editor = "Fernando Orejas and Spirakis, {Paul G.} and {van Leeuwen}, Jan",

booktitle = "Automata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings",

address = "Germany",

note = "28th International Colloquium on Automata, Languages and Programming, ICALP 2001 ; Conference date: 08-07-2001 Through 12-07-2001",

}