Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Labeling Chordal Graphs: Distance Two Condition
SIAM Journal on 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)
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
Graph classes: a survey
Efficient use of radio spectrum in wireless networks with channel separation between close stations
DIALM '00 Proceedings of the 4th international workshop on Discrete algorithms and methods for mobile computing and communications
L(2, 1)-Coloring Matrogenic Graphs
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Graph labeling and radio channel assignment
Journal of Graph Theory
Discrete Applied Mathematics
New bounds for the L(h, k) number of regular grids
International Journal of Mobile Network Design and Innovation
Bounds for the L(d, 1): number of diameter 2 graphs, trees and cacti
International Journal of Mobile Network Design and Innovation
Labelling planar graphs without 4-cycles with a condition on distance two
Discrete Applied Mathematics
A general approach to L(h,k)-label interconnection networks
Journal of Computer Science and Technology
L(j,k)-labelling and maximum ordering-degrees for trees
Discrete Applied Mathematics
k-L(2,1)-labelling for planar graphs is NP-complete for k≥4
Discrete Applied Mathematics
The surviving rate of an outerplanar graph for the firefighter problem
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
Sharp bounds for Zagreb indices of maximal outerplanar graphs
Journal of Combinatorial Optimization
L(h,1,1)-Labeling of outerplanar graphs
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Labeling outerplanar graphs with maximum degree three
Discrete Applied Mathematics
On L(2,1)-labeling of generalized Petersen graphs
Journal of Combinatorial Optimization
On (s,t)-relaxed L (2,1)-labelings of the square lattice
Information Processing Letters
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L(h, 1)-labeling, h = 0, 1, 2, is a class of coloring problems arising from frequency assignment in radio networks, in which adjacent nodes must receive colors that are at least h apart while nodes connected by a two long path must receive different colors. This problem is NP-complete even when limited to planar graphs. Here, we focus on L(h, 1)-labeling restricted to regular tilings of the plane and to outerplanar graphs. We give a unique parametric algorithm labeling each regular tiling of the plane. For these networks, a channel can be assigned to any node in constant time, provided that relative positions of the node in the network is locally known. Regarding outerplanar graphs with maximum degree Δ, we improve the best known upper bounds from Δ + 9, Δ + 5 and Δ + 3 to Δ + 3, Δ + 1 and Δ colors for the values of h equal to 2, 1 and 0, respectively, for sufficiently large values of Δ. For h = 0, 1 this result proves the polinomiality of the problem for outerplanar graphs. Finally, we study the special case Δ = 3, achieving surprising results.