Name
Abstract | ||
|---|---|---|
Given an integer valued weighting of all elements of a 2-connected plane graph G with vertex set V, let c(v) denote the sum of the weight of v is an element of V and of the weights of all edges and all faces incident with v. This vertex coloring of G is proper provided that c(u) not equal c(v) for any two adjacent vertices u and v of G. We show that for every 2-connected plane graph there is such a proper vertex coloring with weights in {1, 2, 3}. In a special case, the value 3 is improved to 2. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.7151/dmgt.1771 | DISCUSSIONES MATHEMATICAE GRAPH THEORY |
Keywords | Field | DocType |
plane graph,vertex coloring | Discrete mathematics,Incidence structure,Combinatorics,Vertex (geometry),Vertex (graph theory),Neighbourhood (graph theory),Nowhere-zero flow,Greedy coloring,1-planar graph,Mathematics,Planar graph | Journal |
Volume | Issue | ISSN |
34 | 4 | 1234-3099 |
Citations | PageRank | References |
2 | 0.40 | 5 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Igor Fabrici | 1 | 101 | 14.64 |
| Jochen Harant | 2 | 217 | 30.62 |
| Stanislav Jendrol' | 3 | 283 | 38.72 |
| Roman Soták | 4 | 128 | 24.06 |