English

Multi-triangulations as complexes of star polygons

Combinatorics 2012-06-14 v2

Abstract

Maximal (k+1)(k+1)-crossing-free graphs on a planar point set in convex position, that is, kk-triangulations, have received attention in recent literature, with motivation coming from several interpretations of them. We introduce a new way of looking at kk-triangulations, namely as complexes of star polygons. With this tool we give new, direct, proofs of the fundamental properties of kk-triangulations, as well as some new results. This interpretation also opens-up new avenues of research, that we briefly explore in the last section.

Keywords

Cite

@article{arxiv.0706.3121,
  title  = {Multi-triangulations as complexes of star polygons},
  author = {Vincent Pilaud and Francisco Santos},
  journal= {arXiv preprint arXiv:0706.3121},
  year   = {2012}
}
R2 v1 2026-06-21T08:40:37.614Z