Simulated annealing: theory and applications
Simulated annealing: theory and applications
Chromatic number of prime distance graphs
2nd Twente workshop on Graphs and combinatorial optimization
Graph Theory With Applications
Graph Theory With Applications
On the packing chromatic number of Cartesian products, hexagonal lattice, and trees
Discrete Applied Mathematics
Fractional chromatic number of distance graphs generated by two-interval sets
European Journal of Combinatorics
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
Note: A note on S-packing colorings of lattices
Discrete Applied Mathematics
The packing coloring of distance graphs D(k,t)
Discrete Applied Mathematics
| Hi-index | 0.04 |
The packing chromatic number @g"@r(G) of a graph G is the smallest integer k such that vertices of G can be partitioned into disjoint classes X"1,...,X"k where vertices in X"i have pairwise distance greater than i. We study the packing chromatic number of infinite distance graphs G(Z,D), i.e., graphs with the set Z of integers as vertex set and in which two distinct vertices i,j@?Z are adjacent if and only if |i-j|@?D. In this paper we focus on distance graphs with D={1,t}. We improve some results of Togni who initiated the study. It is shown that @g"@r(G(Z,D))@?35 for sufficiently large odd t and @g"@r(G(Z,D))@?56 for sufficiently large even t. We also give a lower bound 12 for t=9 and tighten several gaps for @g"@r(G(Z,D)) with small t.