| Multi-triangulations as complexes of starpolygons (2009) | |||||||||||||||
Abstract | |||||||||||||||
| Abstract. Maximal (k+1)-crossing-free graphs on a planar point set in convex position, that is, k-triangulations, have received attention in recent literature, with motivation coming from 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. 1. | |||||||||||||||
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