On the packing chromatic number of Cartesian products, hexagonal lattice, and trees
Discrete Applied Mathematics
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
The packing coloring problem for lobsters and partner limited graphs
Discrete Applied Mathematics
Note: A note on S-packing colorings of lattices
Discrete Applied Mathematics
The packing coloring of distance graphs D(k,t)
Discrete Applied Mathematics
On packing colorings of distance graphs
Discrete Applied Mathematics
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The packing chromatic number @g"@r(G) of a graph G is the smallest integer k such that the vertex set V(G) can be partitioned into disjoint classes X"1,...,X"k, where vertices in X"i have pairwise distance greater than i. For the Cartesian product of a path and the two-dimensional square lattice it is proved that @g"@r(P"m@?Z^2)=~ for any m=2, thus extending the result @g"@r(Z^3)=~ of [A. Finbow, D.F. Rall, On the packing chromatic number of some lattices, Discrete Appl. Math. (submitted for publication) special issue LAGOS'07]. It is also proved that @g"@r(Z^2)=10 which improves the bound @g"@r(Z^2)=9 of [W. Goddard, S.M. Hedetniemi, S.T. Hedetniemi, J.M. Harris, D.F. Rall, Broadcast chromatic numbers of graphs, Ars Combin. 86 (2008) 33-49]. Moreover, it is shown that @g"@r(G@?Z)=6.