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)-labeling of planar graphs
DIALM '01 Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications
Channel assignment and graph labeling
Handbook of wireless networks and mobile computing
On generalized Petersen graphs labeled with a condition at distance two
Discrete Mathematics
Channel Assignment with Separation for Special Classes of Wireless Networks: Grids and Rings
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
IWDC '02 Proceedings of the 4th International Workshop on Distributed Computing, Mobile and Wireless Computing
Complexity of Partial Covers of Graphs
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
L(2, 1)-Coloring Matrogenic Graphs
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Distance-two labelings of graphs
European Journal of Combinatorics
Channel Assignment with Separation for Interference Avoidance in Wireless Networks
IEEE Transactions on Parallel and Distributed Systems
Labeling trees with a condition at distance two
Discrete Mathematics
Discrete Applied Mathematics
L(h,1)-labeling subclasses of planar graphs
Journal of Parallel and Distributed Computing
L(2, 1)-labeling of direct product of paths and cycles
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Generalized list T-colorings of cycles
Discrete Applied Mathematics
A note on collections of graphs with non-surjective lambda labelings
Discrete Applied Mathematics
List version of L(d, s)-labelings
Theoretical Computer Science - Graph colorings
The L(2, 1)-labelling of trees
Discrete Applied Mathematics
L(2, 1)-labelings of Cartesian products of two cycles
Discrete Applied Mathematics
The 2-dipath chromatic number of Halin graphs
Information Processing Letters
Discrete Applied Mathematics
Distance-two labelings of digraphs
Discrete Applied Mathematics
Labeling planar graphs with a condition at distance two
European Journal of Combinatorics
(2,1)-Total labelling of outerplanar graphs
Discrete Applied Mathematics
New bounds for the L(h, k) number of regular grids
International Journal of Mobile Network Design and Innovation
Note: Improved upper bounds on the L(2,1) -labeling of the skew and converse skew product graphs
Theoretical Computer Science
Labelling planar graphs without 4-cycles with a condition on distance two
Discrete Applied Mathematics
On L(d,1)-labeling of Cartesian product of a cycle and a path
Discrete Applied Mathematics
Distance-two labellings of Hamming graphs
Discrete Applied Mathematics
A general approach to L(h,k)-label interconnection networks
Journal of Computer Science and Technology
Distance constrained labelings of planar graphs with no short cycles
Discrete Applied Mathematics
Graph labellings with variable weights, a survey
Discrete Applied Mathematics
Labeling the r-path with a condition at distance two
Discrete Applied Mathematics
Notes: A note on collections of graphs with non-surjective lambda labelings
Discrete Applied Mathematics
Generalized list T-colorings of cycles
Discrete Applied Mathematics
L(2,1)-labeling of direct product of paths and cycles
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Note: The L(2,1)-labelling of trees
Discrete Applied Mathematics
L(2,1)-labelings of Cartesian products of two cycles
Discrete Applied Mathematics
Channel assignment for interference avoidance in honeycomb wireless networks
Journal of Parallel and Distributed Computing
L(j,k)-labelling and maximum ordering-degrees for trees
Discrete Applied Mathematics
Note: L(2,1)-Labelings on the composition of n graphs
Theoretical Computer Science
New upper bounds on the L(2,1)-labeling of the skew and converse skew product 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
On the computational complexity of the L(2,1)-labeling problem for regular graphs
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
On backbone coloring of graphs
Journal of Combinatorial Optimization
Generating and radiocoloring families of perfect graphs
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
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
L(2,1)-labeling of dually chordal graphs and strongly orderable graphs
Information Processing Letters
Labeling Planar Graphs without 4,5-Cycles with a Condition on Distance Two
SIAM Journal on Discrete Mathematics
Labeling outerplanar graphs with maximum degree three
Discrete Applied Mathematics
On the L(h, k)-labeling of co-comparability graphs
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Path covering number and L(2,1)-labeling number of graphs
Discrete Applied Mathematics
List backbone colouring of graphs
Discrete Applied Mathematics
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An $L(2,1)$-labelling of a graph $G$ is an assignment of nonnegative integers to the vertices of $G$ such that adjacent vertices get numbers at least two apart, and vertices at distance two get distinct numbers. The $L(2,1)$-labelling number of $G$, $\lambda(G)$, is the minimum range of labels over all such labellings. It is shown that, for chordal graphs $G$ with minimum degree $\Delta(G)m \lambda(G)\leq(\Delta(G)=3^{2}/4$; in particular, if $G$ is a unit interval graph with chromatic number $\chi(G), \lambda(G)\leq 2\chi(G)$, which is a better bound. As a consequence, it is shown that the conjecture $\lambda(G)\leq\Delta^{2}(G)$ by Griggs and Yeh [SIAM J. Discrete Math., 5(1992), pp. 586-595] is true for chordal graphs.