Distributed Nodes Organization Algorithm for Channel Access in a Multihop Dynamic Radio Network
IEEE Transactions on Computers
Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
Labeling Chordal Graphs: Distance Two Condition
SIAM Journal on Discrete Mathematics
Relating path coverings to vertex labellings with a condition at distance two
Discrete Mathematics
On the $\lambda$-Number of $Q_n$ and Related Graphs
SIAM Journal on Discrete Mathematics
Code assignment for hidden terminal interference avoidance in multihop packet radio networks
IEEE/ACM Transactions on Networking (TON)
On the size of graphs labeled with condition at distance two
Journal of Graph Theory
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
Journal of Algorithms
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Graph classes: a survey
Assigning codes in wireless networks: bounds and scaling properties
Wireless Networks
Channel Assignment for Wireless Networks Modelled as d-Dimensional Square Grids
IWDC '02 Proceedings of the 4th International Workshop on Distributed Computing, Mobile and Wireless Computing
L(2, 1)-Coloring Matrogenic Graphs
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
On Universally Polynomial Context-Free Languages
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Frequency Channel Assignment on Planar Networks
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Online and Offline Distance Constrained Labeling of Disk Graphs
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Labelling of some planar graphs with a condition at distance two
Journal of Applied Mathematics and Computing
Labelling planar graphs without 4-cycles with a condition on distance two
Discrete Applied Mathematics
Distance constrained labelings of planar graphs with no short cycles
Discrete Applied Mathematics
Note: L(2,1)-Labelings on the composition of n graphs
Theoretical Computer Science
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
The L(2,1)-labeling of unigraphs
Discrete Applied Mathematics
L(h,1,1)-Labeling of outerplanar graphs
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Generalized powers of graphs and their algorithmic use
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
IWDC'04 Proceedings of the 6th international conference on Distributed Computing
On the approximability of the L(h, k)-labelling problem on bipartite graphs
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
A general framework for coloring problems: old results, new results, and open problems
IJCCGGT'03 Proceedings of the 2003 Indonesia-Japan joint conference on Combinatorial Geometry and Graph Theory
Minimum Span Frequency Assignment Based on a Multiagent Evolutionary Algorithm
International Journal of Swarm Intelligence Research
On channel-discontinuity-constraint routing in wireless networks
Ad Hoc Networks
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A λ-coloring of a graph G is an assignment of colors from the set {0,....,λ} to the vertices of a graph G such that vertices at distance at most two get different colors and adjacent vertices get colors which are at least two apart. The problem of finding λ-colorings with small or optimal λ arises in the context of radio frequency assignment. We show that the problems of finding the minimum λ for planar graphs, bipartite graphs, chordal graphs and split graphs are NP-Complete. We then give approximation algorithms for λ-coloring and compute upperbounds of the best possible λ for outerplanar graphs, planar graphs, graphs of treewidth k, permutation and split graphs. With the exception of the split graphs, all the above bounds for λ are linear in Δ, the maximum degree of the graph. For split graphs, we give a bound of λ ≤1.5+2Δ+2 and show that there are split graphs with λ = Ω(Δ1.5). Similar results are also given for variations of the λ-coloring problem.