L(h,1,1)-Labeling of Outerplanar Graphs

  • Tiziana Calamoneri
  • Emanuele G. Fusco
  • Richard B. Tan
  • Paola Vocca
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4056)


An L(h,1,1)-labeling of a graph is an assignment of labels from the set of integers {0, ⋯, λ} to the vertices of the graph such that adjacent vertices are assigned integers of at least distance h ≥1 apart and all vertices of distance three or less must be assigned different labels. The aim of the L(h,1,1)-labeling problem is to minimize λ, denoted by λ h,1,1 and called span of the L(h,1,1)-labeling.

As outerplanar graphs have bounded treewidth, the L(1,1,1)-labeling problem on outerplanar graphs can be exactly solved in O(n 3), but the multiplicative factor depends on the maximum degree Δ and is too big to be of practical use. In this paper we give a linear time approximation algorithm for computing the more general L(h,1,1)-labeling for outerplanar graphs that is within additive constants of the optimum values.


Planar Graph Chromatic Number Adjacent Vertex Linear Time Algorithm Color Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tiziana Calamoneri
    • 1
  • Emanuele G. Fusco
    • 1
  • Richard B. Tan
    • 2
    • 3
  • Paola Vocca
    • 4
  1. 1.Dipartimento di InformaticaUniversità di Roma “La Sapienza”RomeItaly
  2. 2.Institute of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands
  3. 3.Department of Computer ScienceUniversity of Sciences & Arts of OklahomaChickashaU.S.A.
  4. 4.Dipartimento di Matematica “Ennio de Giorgi”Università diegli Studi di LecceLecceItaly

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