Easy problems for tree-decomposable graphs
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Journal of Functional Programming
On the packing chromatic number of Cartesian products, hexagonal lattice, and trees
Discrete Applied Mathematics
Parameterized Complexity
The packing chromatic number of infinite product graphs
European Journal of Combinatorics
Packing chromatic number of distance graphs
Discrete Applied Mathematics
The packing coloring problem for (q,q-4) graphs
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
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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Packing coloring is a partitioning of the vertex set of a graph with the property that vertices in the i-th class have pairwise distance greater than i. The main result of this paper is a solution of an open problem of Goddard et al. showing that the decision whether a tree allows a packing coloring with at most k classes is NP-complete. We further discuss specific cases when this problem allows an efficient algorithm. Namely, we show that it is decideable in polynomial time for graphs of bounded treewidth and diameter, and fixed parameter tractable for chordal graphs. We accompany these results by several observations on a closely related variant of the packing coloring problem, where the lower bounds on the distances between vertices inside color classes are determined by an infinite nondecreasing sequence of bounded integers.