Abstract
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 V 1 , V 2 , … , V m where V i is an i -packing for each i . It is proved that the planar triangular lattice T and the three-dimensional integer lattice Z 3 do not have finite packing chromatic numbers.
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