Complexity of the Packing Coloring Problem for Trees

Authors:
Jiří Fiala;Petr A. Golovach
Affiliations:
Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University, Prague, Czech Republic;Department of Informatics, University of Bergen, Bergen, Norway 5020
Venue:
Graph-Theoretic Concepts in Computer Science
Year:
2008

Citing 5
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Abstract

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 . We solve an open problem of Goddard et al. and show that the decision whether a tree allows a packing coloring with at most k classes is NP-complete. We accompany this NP-hardness result by a polynomial time algorithm for trees for 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.