# The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography

@article{Calamoneri2006TheLK, title={The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography}, author={Tiziana Calamoneri}, journal={Comput. J.}, year={2006}, volume={49}, pages={585-608} }

Given any fixed non-negative integer values h and k, the L(h, k)-labelling problem consists in an assignment of non-negative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2 length path receive values which differ by at least k. The span of an L(h, k)-labelling is the difference between the largest and the smallest assigned frequency. The goal of the problem is to find out an L(h, k)-labelling with minimum span. The…

## 154 Citations

### The L(h, k)-Labelling Problem: An Updated Survey and Annotated Bibliography

- Computer ScienceComput. J.
- 2011

The goal of the problem is to find out an L(h, k)-labelling with a minimum span, concerning both the values of h and k and the considered classes of graphs.

### On the L(h, k)-Labeling of Co-comparability Graphs

- Mathematics, Computer ScienceESCAPE
- 2007

The first upper bounds on the L(h, k)-number of co-comparability graphs and interval graphs are provided, in a constructive way, and the result improves on the best previously-known approximation ratio for interval graphs.

### On the L(h, k)-labeling of co-comparability graphs and circular-arc graphs

- Mathematics, Computer Science
- 2009

This article provides the first algorithm to L(h, k)-label co-comparability, interval, and circular-arc graphs with a bounded number of colors and improves on the best previously-known ones using a number of Colors that is at most twice the optimum.

### On the Approximability of the L(h, k)-Labelling Problem on Bipartite Graphs (Extended Abstract)

- Mathematics, Computer ScienceSIROCCO
- 2005

It is proved that the L(h,k) – labelling problem is not easier than coloring the square of a graph, and an approximation algorithm with performance ratio bounded by $\frac{4}{3} D^2$, where, D is equal to the minimum even value bounding the minimum of the maximum degrees of the two partitions.

### A General Approach to L(h,k)-Label Interconnection Networks

- Computer ScienceJournal of Computer Science and Technology
- 2008

A general algorithm for L(h, k)-labeling these graphs is presented, and from this method an efficient L(2, 1) -labeling for Butterfly and CCC networks is derived.

### New bounds for the L(h, k) number of regular grids

- Mathematics
- 2006

The L (h, k)-labelling problem on regular grids of degree 3, 4 and 6 for those values of h and k whose λh,k is either not known or not tight is studied.

### L(h, 1, 1)-labeling of outerplanar graphs

- Mathematics, Computer ScienceMath. Methods Oper. Res.
- 2006

A linear time approximation algorithm is given for computing the more general L(h, 1, 1)-labeling for outerplanar graphs that is within additive constants of the optimum values.

### L(2, 1)-Labeling of Unigraphs - (Extended Abstract)

- Mathematics, Computer ScienceTAPAS
- 2011

A 3/2-approximate algorithm for L(2, 1)-labeling unigraphs is designed and it is designed that runs in O(n) time, improving the time of the algorithm based on the greedy technique, requiring O(m)Time, that may be near to Θ(n2) for unigraphing.

## References

SHOWING 1-10 OF 158 REFERENCES

### A General Approach to L(h,k)-Label Interconnection Networks

- Computer ScienceJournal of Computer Science and Technology
- 2008

A general algorithm for L(h, k)-labeling these graphs is presented, and from this method an efficient L(2, 1) -labeling for Butterfly and CCC networks is derived.

### Fixed-Parameter Complexity of lambda-Labelings

- MathematicsWG
- 1999

It is shown that for every fixed value k ≥ 4 it is NP-complete to determine whether λ(G) ≤ k, and several hardness results for L(G; p, q) are shown, including that for any p > q ≥ 1 there is a λ = λ (p,q) such that deciding if L(P; p; p) ≤ κ(p,Q) isNP-complete.

### On labeling the vertices of products of complete graphs with distance constraints

- Mathematics
- 2005

Variations of Hale's channel assignment problem, the L(j, k)‐labeling problem and the radio labeling problem require the assignment of integers to the vertices of a graph G subject to various…

### On the Computational Complexity of the L(2, 1)-Labeling Problem for Regular Graphs

- MathematicsICTCS
- 2005

It is shown that for all k ≥ 3, the decision problem whether a k-regular graph admits an L(2,1)-labeling of span k+2 is NP-complete.