On colorings of squares of outerplanar graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A bound on the chromatic number of the square of a planar graph
Journal of Combinatorial Theory Series B
Algorithms for finding distance-edge-colorings of graphs
Journal of Discrete Algorithms
Labeling planar graphs with a condition at distance two
European Journal of Combinatorics
Approximating the L(h, k)-labelling problem
International Journal of Mobile Network Design and Innovation
Coloring squares of planar graphs with girth six
European Journal of Combinatorics
Vertex coloring acyclic digraphs and their corresponding hypergraphs
Discrete Applied Mathematics
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
A unified approach to distance-two colouring of planar graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
List 2-distance (Δ+2)-coloring of planar graphs with girth six
European Journal of Combinatorics
A general approach to L(h,k)-label interconnection networks
Journal of Computer Science and Technology
Parameterized Complexity of Coloring Problems: Treewidth versus Vertex Cover
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
SIAM Journal on Scientific Computing
Parameterized complexity of coloring problems: Treewidth versus vertex cover
Theoretical Computer Science
Generalized powers of graphs and their algorithmic use
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Algorithms for finding distance-edge-colorings of graphs
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Strong colorings of hypergraphs
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Sufficient sparseness conditions for G2 to be (Δ+1)-choosable, when Δ≥5
Discrete Applied Mathematics
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We give nontrivial bounds for the inductiveness or degeneracy of power graphs Gk of a planar graph G. This implies bounds for the chromatic number as well, since the inductiveness naturally relates to a greedy algorithm for vertex-coloring the given graph. The inductiveness moreover yields bounds for the choosability of the graph. We show that the inductiveness of a square of a planar graph G is at most $\lceil 9\Delta /5 \rceil$, for the maximum degree $\Delta$ sufficiently large, and that it is sharp. In general, we show for a fixed integer $k\geq1$ the inductiveness, the chromatic number, and the choosability of Gk to be $O(\Delta^{\lfloor k/2 \rfloor})$, which is tight.