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 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.
This work was partially supported by the Università di Roma “La Sapienza”, Italy.
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Calamoneri, T., Fusco, E.G., Tan, R.B., Vocca, P. (2006). L(h,1,1)-Labeling of Outerplanar Graphs. In: Flocchini, P., Gąsieniec, L. (eds) Structural Information and Communication Complexity. SIROCCO 2006. Lecture Notes in Computer Science, vol 4056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780823_21
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DOI: https://doi.org/10.1007/11780823_21
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