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L(2,1,1)-labeling is NP-complete for trees.

Golovach, P.A. and Lidicky, B. and Paulusma, Daniel (2010) 'L(2,1,1)-labeling is NP-complete for trees.', in Theory and applications of mdels of computation, 7th Annual Conference, TAMC 2010, 7-11 June 2010, Prague, Czech Republic ; proceedings. Berlin ; Heidelburg: Springer, pp. 211-221. Lecture notes in computer science. (6108).


An L(p 1,p 2,p 3)-labeling of a graph G with span λ is a mapping f that assigns each vertex u of G an integer label 0 ≤ f(u) ≤ λ such that |f(u) − f(v)| ≥ p i whenever vertices u and v are of distance i for i ∈ {1,2,3}. We show that testing whether a given graph has an L(2,1,1)-labeling with some given span λ is NP-complete even for the class of trees.

Item Type:Book chapter
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Date of first online publication:2010
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