L(h,1,1)-Labeling of outerplanar graphs

  • Authors:

  • Tiziana Calamoneri;Emanuele G. Fusco;Richard B. Tan;Paola Vocca

  • Affiliations:

  • Dipartimento di Informatica, Università di Roma “La Sapienza”, Rome, Italy;Dipartimento di Informatica, Università di Roma “La Sapienza”, Rome, Italy;Institute of Information and Computing Sciences, Utrecht University, Utrecht, CH, The Netherlands;Dipartimento di Matematica “Ennio de Giorgi”, Università diegli Studi di Lecce, Lecce, Italy

  • Venue:
  • SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
  • Year:
  • 2006

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Abstract

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 λh,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(n3), 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