L(2,1)-labeling of unigraphs

Authors:
Tiziana Calamoneri;Rossella Petreschi
Affiliations:
Department of Computer Science, "Sapienza" University of Rome - Italy;Department of Computer Science, "Sapienza" University of Rome - Italy
Venue:
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Year:
2011

Citing 11
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Abstract

The L(2, 1)-labeling problem consists of assigning colors from the integer set 0, ..., λ to the nodes of a graph G in such a way that nodes at a distance of at most two get different colors, while adjacent nodes get colors which are at least two apart. The aim of this problem is to minimize λ and it is in general NP-complete. In this paper the problem of L(2, 1)-labeling unigraphs, i.e. graphs uniquely determined by their own degree sequence up to isomorphism, is addressed and a 3/2-approximate algorithm for L(2, 1)-labeling unigraphs is designed. This algorithm runs in O(n) time, improving the time of the algorithm based on the greedy technique, requiring O(m) time, that may be near to Θ(n2) for unigraphs.