On the packing chromatic number of some lattices
- Resource Type
- Article
- Authors
- Finbow, Arthur S.; Rall, Douglas F.
- Source
- Discrete Applied Mathematics. Jun2010, Vol. 158 Issue 12, p1224-1228. 5p.
- Subject
- *GRAPH coloring
*LATTICE theory
*INTEGER programming
*PARTITIONS (Mathematics)
*COMBINATORICS
- Language
- ISSN
- 0166-218X
Abstract: For a positive integer , a -packing in a graph is a subset of vertices such that the distance between any two distinct vertices from is more than . The packing chromatic number of is the smallest integer such that the vertex set of can be partitioned as where is an -packing for each . It is proved that the planar triangular lattice and the three-dimensional integer lattice do not have finite packing chromatic numbers. [Copyright &y& Elsevier]