Counting triangulations of planar point sets

Micha Sharir*, Adam Sheffer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

50 Scopus citations

Abstract

We study the maximal number of triangulations that a planar set of n points can have, and show that it is at most 30n. This new bound is achieved by a careful optimization of the charging scheme of Sharir and Welzl (2006), which has led to the previous best upper bound of 43n for the problem. Moreover, this new bound is useful for bounding the number of other types of planar (i.e., crossing-free) straight-line graphs on a given point set. Specifically, it can be used to derive new upper bounds for the number of planar graphs (207.84n), spanning cycles (O(68.67n)), spanning trees (O(146.69n)), and cycle-free graphs (O(164.17n)).

Original languageEnglish
JournalElectronic Journal of Combinatorics
Volume18
Issue number1
DOIs
StatePublished - 2011

Keywords

  • Charging schemes
  • Counting
  • Crossing-free graphs
  • Triangulations

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