Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Scheduling algorithms for multihop radio networks
IEEE/ACM Transactions on Networking (TON)
On the $\lambda$-Number of $Q_n$ and Related Graphs
SIAM Journal on Discrete Mathematics
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
Coloring powers of planar graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A new bound on the cyclic chromatic number
Journal of Combinatorial Theory Series B
On the Complexity of Distance-2 Coloring
ICCI '92 Proceedings of the Fourth International Conference on Computing and Information: Computing and Information
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Graph labeling and radio channel assignment
Journal of Graph Theory
IWDC '02 Proceedings of the 4th International Workshop on Distributed Computing, Mobile and Wireless Computing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Labeling planar graphs with a condition at distance two
European Journal of Combinatorics
New bounds for the L(h, k) number of regular grids
International Journal of Mobile Network Design and Innovation
Coloring squares of planar graphs with girth six
European Journal of Combinatorics
List 2-distance (Δ+2)-coloring of planar graphs with girth six
European Journal of Combinatorics
Graph labellings with variable weights, a survey
Discrete Applied Mathematics
A sequential approach for optimal broadcast scheduling in packet radio networks
IEEE Transactions on Communications
Algorithms and experiments on colouring squares of planar graphs
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
Sleeping schedule-aware minimum latency broadcast in wireless ad hoc networks
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
A probabilistic greedy algorithm for channel assignment in cellular radio networks
IEEE Transactions on Communications
Strong colorings of hypergraphs
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Frequency assignment and multicoloring powers of square and triangular meshes
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
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For integers p 驴 q, a L(p, q)-labeling of a network G is an integer labeling of the nodes of G such that adjacent nodes receive integers which differ by at least p, and nodes at distance two receive labels which differ by at least q. The minimum number of labels required in such labeling is 驴qp(G). This arises in the context of frequency channel assignment in mobile and wireless networks and often G is planar. We show that if G is planar then 驴qp(G) 驴 5/3 (2q - 1)驴 + 12p + 144q - 78. We also provide an O(n2) time algorithm to find such a labeling. This provides a (5/3 + o(1))-approximation algorithm for the interesting case of q = 1, improving the best previous approximation ratio of 2.