Acyclic and k-distance coloring of the grid
Information Processing Letters
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
Complexity of the packing coloring problem for trees
Discrete Applied Mathematics
On the packing chromatic number of some lattices
Discrete Applied Mathematics
Packing chromatic number of distance graphs
Discrete Applied Mathematics
| Hi-index | 0.04 |
Let a"1,a"2,...,a"k be positive integers. An (a"1,a"2,...,a"k)-packing coloring of a graph G is a mapping from V(G) to {1,2,...,k} such that vertices with color i have pairwise distance greater than a"i. In this paper, we study (a"1,a"2,...,a"k)-packing colorings of several lattices including the infinite square, triangular, and hexagonal lattices. For k small, we determine all a"i such that these graphs have packing colorings. We also give some exact values and asymptotic bounds.