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Abstract: Maximal $k+1$-crossing-free graphs on a planar point set in convexposition, that is, $k$-triangulations, have received attention in recentliterature, with motivation coming from several interpretations of them.We introduce a new way of looking at $k$-triangulations, namely as complexesof star polygons. With this tool we give new, direct, proofs of the fundamentalproperties of $k$-triangulations, as well as some new results. Thisinterpretation also opens-up new avenues of research, that we briefly explorein the last section.



Autor: Vincent Pilaud, Francisco Santos

Fuente: https://arxiv.org/







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