Multitriangulations as Complexes of Star Polygons

Discrete & Computational Geometry - Tập 41 - Trang 284-317 - 2008
Vincent Pilaud1, Francisco Santos2
1Département d’Informatique, École Normale Supérieure, Paris, France
2Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Santander, Spain

Tóm tắt

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.

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