Multitriangulations as complexes of star-polygons

Vincent Pilaud (1) , Francisco Santos (2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 MATESCO - Departamento de Matemáticas, Estadística y Computación

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.

Mots clés: Generalized triangulation; Crossing-free graph; Star polygons; Flips; Associahedron

Domaines: Combinatoire [math.CO]

Vincent Pilaud, Francisco Santos. Multitriangulations as complexes of star-polygons. Discrete and Computational Geometry, 2009, 41 (2), pp.284-317. ⟨10.1007/s00454-008-9078-6⟩. ⟨hal-00777889⟩