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

Author

Listed:
  • Tiziana Calamoneri
  • Emanuele Fusco
  • Richard Tan
  • Paola Vocca

Abstract

An L(h, 1, 1)-labeling of a graph is an assignment of labels from the set of integers {0, . . . , λ} to the nodes of the graph such that adjacent nodes are assigned integers of at least distance h ≥ 1 apart and all nodes 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. Copyright Springer-Verlag 2009

Suggested Citation

  • Tiziana Calamoneri & Emanuele Fusco & Richard Tan & Paola Vocca, 2009. "L(h, 1, 1)-labeling of outerplanar graphs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(2), pages 307-321, May.
    • Handle: RePEc:spr:mathme:v:69:y:2009:i:2:p:307-321
    DOI: 10.1007/s00186-008-0261-6
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    Cited by:

    1. Zehui Shao & Aleksander Vesel, 2015. "$$L(3,2,1)$$ L ( 3 , 2 , 1 ) -labeling of triangular and toroidal grids," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(3), pages 659-673, September.

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