Discrete & Computational Geometry

, Volume 41, Issue 2, pp 284–317 | Cite as

Multitriangulations as Complexes of Star Polygons

  • Vincent PilaudEmail author
  • Francisco Santos


Maximal (k+1)-crossing-free graphs on a planar point set in convex position, that is, k-triangulations, have received attention in recent literature, motivated by several interpretations of them.

We introduce a new way of looking at k-triangulations, namely as complexes of star polygons. With this tool we give new, direct proofs of the fundamental properties of k-triangulations, as well as some new results. This interpretation also opens up new avenues of research that we briefly explore in the last section.


Generalized triangulation Crossing-free graph Star polygons Flips Associahedron 


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Département d’InformatiqueÉcole Normale SupérieureParisFrance
  2. 2.Departamento de Matemáticas, Estadística y ComputaciónUniversidad de CantabriaSantanderSpain

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