Multi-triangulations as complexes of star polygons

Details Multi-triangulations as complexes of star polygons Multi-triangulations as complexes of star polygons

2007-06-21

arxiv.org/abs/0706.3121v2

Discrete Comput. Geom., 41(2), 2009, 284-317

Mathematics

Combinatorics

40 pages, 24 figures; added references, update Section 8

Scientific paper

10.1007/s00454-008-9078-6

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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