Multi-triangulations as complexes of star polygons

2007/06/30 by Vincent Pilaud, Francisco Santos · 1 citation
Mathematics · #math.CO #msc:05C62 #msc:52C20 #msc:68U05

paper · pdf · doi:10.1007/s00454-008-9078-6

published as Discrete Comput. Geom., 41(2):284-317, 2009 · 40 pages, 24 figures; added references, update Section 8

arxiv created 2007/09/05 · arxiv updated 2012/06/14

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.

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