Coloring the square of a planar graph

Authors:
Jan van den Heuvel;Sean McGuinness
Affiliations:
Centre for Discrete and Applicable Mathematics, Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom;Department of Mathematics University of Umeå Umeå, Sweden
Venue:
Journal of Graph Theory
Year:
2003

Citing 0
Cited 28

Note: coloring the square of a K4-minor free graph

Discrete Mathematics
The L(2, 1)-labelling of trees

Discrete Applied Mathematics
L(p, q)-labelling of K4-minor free graphs

Information Processing Letters
A bound on the chromatic number of the square of a planar graph

Journal of Combinatorial Theory Series B
Labeling planar graphs with a condition at distance two

European Journal of Combinatorics
Labelling of some planar graphs with a condition at distance two

Journal of Applied Mathematics and Computing
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
A unified approach to distance-two colouring of planar graphs

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Distance constrained labelings of planar graphs with no short cycles

Discrete Applied Mathematics
Note: The L(2,1)-labelling of trees

Discrete Applied Mathematics
L(p,q)-labelling of K4-minor free graphs

Information Processing Letters
A sequential approach for optimal broadcast scheduling in packet radio networks

IEEE Transactions on Communications
k-L(2,1)-labelling for planar graphs is NP-complete for k≥4

Discrete Applied Mathematics
A probabilistic greedy algorithm for channel assignment in cellular radio networks

IEEE Transactions on Communications
New upper bounds on the L(2,1)-labeling of the skew and converse skew product graphs

Theoretical Computer Science
Distributed colorings for collision-free routing in sink-centric sensor networks

Journal of Discrete Algorithms
Survey: Randomly colouring graphs (a combinatorial view)

Computer Science Review
Griggs and Yeh's Conjecture and $L(p,1)$-labelings

SIAM Journal on Discrete Mathematics
Labeling Planar Graphs without 4,5-Cycles with a Condition on Distance Two

SIAM Journal on Discrete Mathematics
Distance coloring and distance edge-coloring of d- dimensional lattice

ICIC'12 Proceedings of the 8th international conference on Intelligent Computing Theories and Applications
An optimal square coloring of planar graphs

Journal of Combinatorial Optimization
L(2,1) -labeling of oriented planar graphs

Discrete Applied Mathematics
A unified approach to distance-two colouring of graphs on surfaces

Combinatorica
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

Quantified Score

Hi-index	0.01

Visualization

Abstract

We prove that for any planar graph G with maximum degree Δ, it holds that the chromatic number of the square of G satisfies χ(G2) ≤ 2Δ + 25. We generalize this result to integer labelings of planar graphs involving constraints on distances one and two in the graph. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 110–124, 2003 Supported in part by the U.K. Radiocommunications Agency.