Name
Abstract | ||
|---|---|---|
A total coloring of a graph G is a coloring of all elements of G, i.e. vertices and edges, such that no two adjacent or incident elements receive the same color. A graph G is s-degenerate 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-degenerate graph G has a total coloring with Δ+1 colors if the maximum degree Δ of G is sufficiently large, say Δ≥4s+3. Our proof yields an efficient algorithm to find such a total coloring. We also give a lineartime algorithm to find a total coloring of a graph G with the minimum number of colors if G is a partial k-tree, that is, the tree-width of G is bounded by a fixed integer k. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/s00493-007-0050-5 | Combinatorica |
Keywords | Field | DocType |
positive integer,maximum degree,trivial graph,total coloring,graph g,incident element,total colorings,degenerate graphs,fixed integer k,efficient algorithm,s-degenerate graph,lineartime algorithm | Discrete mathematics,Edge coloring,Complete coloring,Combinatorics,Total coloring,Graph power,Fractional coloring,List coloring,Greedy coloring,Mathematics,Graph coloring | Journal |
Volume | Issue | ISSN |
27 | 2 | 0209-9683 |
Citations | PageRank | References |
8 | 0.65 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Shuji Isobe | 1 | 28 | 8.28 |
| Xiao Zhou | 2 | 325 | 43.69 |
| Takao Nishizeki | 3 | 1771 | 267.08 |