Flip Graphs of Bounded-Degree Triangulations☆

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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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Cited by (1)

☆

This work was initiated during the Second European Pseudo-Triangulation Working Week in Alcalá de Henares, Spain, 2005.

1

Supported by the FWF [Austrian Fonds zur Förderung der Wissenschaftlichen Forschung] under grant S9205-N12, NFN Industrial Geometry.

2

Partially supported by grants MTM2008-04699-C03-02 and HU2007-0017.

3

Partially supported by the Deutsche Forschungsgemeinschaft (DFG) under grant RO 2338/2-1.

4

Partially supported by the Netherlands' Organisation for Scientific Research (NWO) under project no. 639.022.707.

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