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
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
Coloring Powers of Planar Graphs
SIAM Journal on Discrete Mathematics
Graph labeling and radio channel assignment
Journal of Graph Theory
Coloring the square of a planar graph
Journal of Graph Theory
On colorings of squares of outerplanar graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The L(2, 1)-labelling of trees
Discrete Applied Mathematics
A note on 2-facial coloring of plane graphs
Information Processing Letters
L(p, q)-labelling of K4-minor free graphs
Information Processing Letters
The 2-dipath chromatic number of Halin graphs
Information Processing Letters
Labeling planar graphs with a condition at distance two
European Journal of Combinatorics
(2,1)-Total labelling of outerplanar graphs
Discrete Applied Mathematics
The distant-2 chromatic number of random proximity and random geometric graphs
Information Processing Letters
Coloring squares of planar graphs with girth six
European Journal of Combinatorics
Labelling planar graphs without 4-cycles with a condition on distance two
Discrete Applied Mathematics
Improved Upper Bounds for λ-Backbone Colorings Along Matchings and Stars
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
(2,1)-Total labelling of trees with sparse vertices of maximum degree
Information Processing Letters
A unified approach to distance-two colouring of planar graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Injective coloring of planar graphs
Discrete Applied Mathematics
List 2-distance (Δ+2)-coloring of planar graphs with girth six
European Journal of Combinatorics
(2,1)-Total number of trees with maximum degree three
Information Processing Letters
Distance constrained labelings of planar graphs with no short cycles
Discrete Applied Mathematics
Graph labellings with variable weights, a survey
Discrete Applied Mathematics
Conflict-free colourings of graphs and hypergraphs
Combinatorics, Probability and Computing
Note: The L(2,1)-labelling of trees
Discrete Applied Mathematics
A note on 2-facial coloring of plane graphs
Information Processing Letters
L(p,q)-labelling of K4-minor free graphs
Information Processing Letters
L(j,k)-labelling and maximum ordering-degrees for trees
Discrete Applied Mathematics
The 2-distance coloring of the Cartesian product of cycles using optimal Lee codes
Discrete Applied Mathematics
On backbone coloring of graphs
Journal of Combinatorial Optimization
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
An optimal square coloring of planar graphs
Journal of Combinatorial Optimization
L(2,1) -labeling of oriented planar graphs
Discrete Applied Mathematics
Sufficient sparseness conditions for G2 to be (Δ+1)-choosable, when Δ≥5
Discrete Applied Mathematics
The L(p,q)-labelling of planar graphs without 4-cycles
Discrete Applied Mathematics
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Wegner conjectured that the chromatic number of the square of any planar graph G with maximum degree Δ ≥ 8 is bounded by χ(G2) ≤ ⌊3/2 Δ⌋ + 1. We prove the bound χ(G2) ≤ ⌈5/3 Δ⌉ + 78. This is asymptotically an improvement on the previously best-known bound. For large values of Δ we give the bound of χ(G2) ≤ ⌈5/3 Δ⌉ + 25. We generalize this result to L(p, q)-labeling of planar graphs, by showing that λqp(G) ≤ q ⌈5/3 Δ⌉ + 18p + 77q - 18. For each of the results, the proof provides a quadratic time algorithm.