On properties of random dissections and triangulations

Abstract

In this work we study properties of random graphs that are drawn uniformly at random from the class consisting of biconnected outerplanar graphs, or equivalently dissections of large convex polygons. We obtain very sharp concentration results for the number of vertices of any given degree, and for the number of induced copies of a given fixed graph. Our method gives similar results for random graphs from the class of triangulations of convex polygons.

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Correspondence to Nicla Bernasconi.

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An extended abstract of this work will appear in the Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’ 08).

Tthis work was partially supported by the SNF, grant nr. 20021-107880/1.

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Bernasconi, N., Panagiotou, K. & Steger, A. On properties of random dissections and triangulations. Combinatorica 30, 627–654 (2010). https://doi.org/10.1007/s00493-010-2464-8

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Mathematics Subject Classification (2000)

  • 05C80
  • 05C07