On the packing chromatic number of some lattices

@article{Finbow2010OnTP,
  title={On the packing chromatic number of some lattices},
  author={Art S. Finbow and Douglas F. Rall},
  journal={Discrete Applied Mathematics},
  year={2010},
  volume={158},
  pages={1224-1228}
}
For a positive integer k, a k-packing in a graph G is a subset A of vertices such that the distance between any two distinct vertices from A is more than k. The packing chromatic number of G is the smallest integer m such that the vertex set of G can be partitioned as V1, V2, . . . , Vm where Vi is an i-packing for each i. It is proved that the planar triangular lattice T and the 3-dimensional integer lattice Z do not have finite packing chromatic numbers. 

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