Flip Graphs of Bounded-Degree Triangulations

O Aichholzer,A Schulz,G Rote,B Speckmann,D Orden,P Ramos,T Hackl

doi:10.1016/j.endm.2009.07.084

Flip Graphs of Bounded-Degree Triangulations

O Aichholzer, A Schulz + Show 5 more

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https://doi.org/10.1016/j.endm.2009.07.084

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Journal: Electronic Notes in Discrete Mathematics	Publication Date: Jul 30, 2009
Citations: 1

Affiliation: Graz University of Technology, Software (Germany), Smith College, Freie Universität Berlin, Eindhoven University of Technology, University of Alcalá

#Flip Graphs #Points In Convex Position + Show 8 more

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Abstract

We study flip graphs of triangulations whose maximum vertex degree is bounded by a constant k. Specifically, we consider triangulations of sets of n points in convex position in the plane and prove that their flip graph is connected if and only if k>6; the diameter of the flip graph is O(n2). We also show that for general point sets, flip graphs of triangulations with degree ⩽k can be disconnected for any k.

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