Triangulations without pointed spanning trees

Authors:
Oswin Aichholzer;Clemens Huemer;Hannes Krasser
Affiliations:
Institute for Softwaretechnology, Graz University of Technology, Graz, Austria;Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Barcelona, Spain;Institute for Theoretical Computer Science, Graz University of Technology, Graz, Austria
Venue:
Computational Geometry: Theory and Applications
Year:
2008

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Abstract

Problem 50 in the Open Problems Project of the computational geometry community asks whether any triangulation on a point set in the plane contains a pointed spanning tree as a subgraph. We provide a counterexample. As a consequence we show that there exist triangulations which require a linear number of edge flips to become Hamiltonian.