Abstract
We investigate adjacency labeling schemes for graphs of bounded degree Δ = O(1). In particular, we present an optimal (up to an additive constant) logn + O(1) adjacency labeling scheme for bounded degree trees. The latter scheme is derived from a labeling scheme for bounded degree outerplanar graphs. Our results complement a similar bound recently obtained for bounded depth trees [Fraigniaud and Korman, SODA 2010], and may provide new insights for closing the long standing gap for adjacency in trees [Alstrup and Rauhe, FOCS 2002]. We also provide improved labeling schemes for bounded degree planar graphs. Finally, we use combinatorial number systems and present an improved adjacency labeling schemes for graphs of bounded degree Δ with \((e+1)\sqrt{n} < \Delta \leq n/5\).
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Adjiashvili, D., Rotbart, N. (2014). Labeling Schemes for Bounded Degree Graphs. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds) Automata, Languages, and Programming. ICALP 2014. Lecture Notes in Computer Science, vol 8573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43951-7_32
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DOI: https://doi.org/10.1007/978-3-662-43951-7_32
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