L(2,1,1)-Labeling Is NP-Complete for Trees

  • Petr A. Golovach
  • Bernard Lidický
  • Daniël Paulusma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 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.


Polynomial Time Chromatic Number Vertex Cover Conjunctive Normal Form Truth Assignment 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Petr A. Golovach
    • 1
  • Bernard Lidický
    • 2
  • Daniël Paulusma
    • 1
  1. 1.Department of Computer ScienceUniversity of Durham, Science LaboratoriesDurhamEngland
  2. 2.Faculty of Mathematics and Physics, DIMATIA and Institute for Theoretical Computer Science (ITI)Charles UniversityPragueCzech Republic

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