On the packing chromatic number of some lattices

Authors:
Arthur S. Finbow;Douglas F. Rall
Affiliations:
Department of Mathematics and Computing Science, Saint Mary's University, Halifax, Canada B3H 3C3;Department of Mathematics, Furman University, Greenville, SC 29613, USA
Venue:
Discrete Applied Mathematics
Year:
2010

Citing 1
Cited 4

On the packing chromatic number of Cartesian products, hexagonal lattice, and trees

Discrete Applied Mathematics

The packing chromatic number of infinite product graphs

European Journal of Combinatorics
Packing chromatic number of distance graphs

Discrete Applied Mathematics
Note: A note on S-packing colorings of lattices

Discrete Applied Mathematics
On packing colorings of distance graphs

Discrete Applied Mathematics

Quantified Score

Hi-index	0.04

Visualization

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.