Perfect $k$-Colored Matchings and $(k+2)$-Gonal Tilings

Oswin Aichholzer, Lukas Andritsch, Karin Baur, Birgit Vogtenhuber

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We derive a simple bijection between geometric plane perfect matchings on $2n$ points in convex position and triangulations on $n+2$ points in convex position. We then extend this bijection to monochromatic plane perfect matchings on periodically $k$-colored vertices and $(k+2)$-gonal tilings of convex point sets. These structures are related to a generalization of Temperley–Lieb algebras and our bijections provide explicit one-to-one relations between matchings and tilings. Moreover, for a given element of one class, the corresponding element of the other class can be computed in linear time.
Original languageEnglish
Pages (from-to)1333-1346
Number of pages14
JournalGraphs and Combinatorics
Issue number6
Publication statusPublished - 2018

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