• Corpus ID: 5656269

Approximations for λ-Colorings of Graphs 201

@inproceedings{Bodlaender2004ApproximationsF,
  title={Approximations for $\lambda$-Colorings of Graphs 201},
  author={Hans L. Bodlaender and Ton Kloks and Richard B. Tan and Jan van Leeuwen},
  year={2004}
}
A λ-coloring of a graph G is an assignment of colors from the integer set {0, . . . , λ} to the vertices of the graph G such that vertices at distance of at most two get different colors and adjacent vertices get colors which are at least two apart. The problem of finding λ-colorings with optimal or near-optimal λ arises in the context of radio frequency assignment. We show that the problem of finding the minimum λ for planar graphs, bipartite graphs, chordal graphs and split graphs is NP… 

Figures from this paper

ETH Library On the Advice Complexity of the Online L(2, 1)-Coloring Problem on Paths and Cycles

The L(2, 1)-coloring problem is the first known example of an online problem for which sublinear advice does not help and it is proved that no randomized online algorithm can achieve a better expected competitive ratio than 4 (1− δ), for any δ > 0.

Complexity of Locally Injective k-Colourings of Planar Graphs

A colouring of the vertices of a graph is called injective if every two distinct vertices connected by a path of length 2 receive different colours, and it is called locally injective if it is an

L(2, 1)-Labeling of Permutation and Bipartite Permutation Graphs

The upper bound for permutation graphs to max is improved to max by doing a detailed analysis of Chang and Kuo’s heuristic for L(2, 1)-labeling of general graphs applied to the particular case of permutations graphs.

List version of L(d, s)-labelings

L(0,1)-labelling of Permutation Graphs

It is shown that, for a permutations graph G with maximum vertex degree Δ, the upper bound of λ0,1(G) is Δ−1 and it is proved that the result is exact for bipartite permutation graph.

On $$(s,t)$$(s,t)-relaxed $$L(2,1)$$L(2,1)-labeling of graphs

A new graph parameter called the breaking path covering number of a graph is introduced, and basic properties of the relaxed L(2,1)$$L( 2,1)-labeling numbers of graphs and trees are discussed.

\(L(2,1)\)-Labeling of Cartesian Product of Complete Bipartite Graph and Path

An \(L(2,1)\)-labeling problem is a particular case of \(L(h,k)\)-labeling problem. An \(L(2,1)\)-labeling of a graph \(G=(V,E)\) is a function \(f\) from the set of vertices \(V\) to the set of

References

SHOWING 1-10 OF 45 REFERENCES

Approximations for -Coloring of Graphs

It is shown that the problem of finding the minimum λ for planar graphs, bipartite graphs, chordal graphs and split graphs are NP-Complete and approximation algorithms for λ-coloring are given and upper bounds of the best possible λ are computed.

Generalized Vertex-Colorings of Partial K-Trees

Let l be a positive integer, and let G be a graph with nonnegative integer weights on edges. Then a generalized vertex-coloring, called an l-coloring of G, is an assignment of colors to the vertices

L(2,1)-labeling of planar graphs

This paper improves the best known upper bound from Δ + 9 to Δ + 3 colors, Δ being the maximum degree of the graph and Δ ⪈ 8.

NP-Completeness Results and Efficient Approximations for Radiocoloring in Planar Graphs

This paper proves that the min span RCP is NP-complete for planar graphs and provides an O(nΔ) time algorithm which obtains a radiocoloring of a planar graph G that approximates the minimum order within a ratio which tends to 2.

L(2, 1)-Coloring Matrogenic Graphs

Improvements on previously known results concerning subclasses of cographs, split graphs and graphs with diameter two are achieved in this problem of assigning channels to the stations of a wireless network when the graph representing the possible interferences is a matrogenic graph.

THE EDGE SPAN OF DISTANCE TWO LABELLINGS OF GRAPHS

A graph labelling problem which has two constraints instead of one is proposed and the question of finding the minimum edge of this labelling is considered.

Relating path coverings to vertex labellings with a condition at distance two

Labeling graphs with a condition at distance two

The problem arises from the channel assignment problem. An L(2, 1)-labeling of a graph G = (V, E) is a function f : V → {0, 1, 2, . . .} such that |f(x) − f(y)| ≤ 2 if d(x, y) = 2 and |f(x) − f(y)| ≤

Some Simplified NP-Complete Graph Problems

On L(d, 1)-labelings of graphs