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Discrete Mathematics & Theoretical Computer Science |
A $k$-triangulation of a convex polygon is a maximal set of diagonals so that no $k+1$ of them mutually cross. $k$-triangulations have received attention in recent literature, with motivation coming from several interpretations of them. We present a new way of looking at $k$-triangulations, where certain star polygons naturally generalize triangles for $k$-triangulations. With this tool we give new, direct proofs of the fundamental properties of $k$-triangulations (number of edges, definition of flip). This interpretation also opens up new avenues of research that we briefly explore in the last section.
Source : ScholeXplorer
IsRelatedTo ARXIV 1009.4690 Source : ScholeXplorer IsRelatedTo DOI 10.37236/1167 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1009.4690
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