Transforming Triangulations on Nonplanar Surfaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2010Embargo end date: 01 Jan 2003 Spain English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Discrete Mathematics, volume 24, pages 821-840 (issn: 0895-4801, eissn: 1095-7146,

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Authors: Carmen Cortés; Clara I. Grima; Ferran Hurtado; Alberto Márquez 0001; Francisco Santos; Jesus Valenzuela;

doi: 10.1137/070697987 , 10.48550/arxiv.math/0311228 , 10.13140/rg.2.2.23184.99848

arXiv: math/0311228

handle: 11441/33408 , 10902/27546 , 11441/34842

Transforming Triangulations on Nonplanar Surfaces

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Abstract

We consider whether any two triangulations of a polygon or a point set on a non-planar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some remarkable exceptions, such as polygons on the cylinder, and on the flat torus, and certain configurations of points on the cylinder.

19 pages, 17 figures. This version has been accepted in the SIAM Journal on Discrete Mathematics. Keywords: Graph of triangulations, triangulations on surfaces, triangulations of polygons, edge flip

Country

Spain

Related Organizations

University of Seville
Spain
University of Cantabria
Spain

Keywords

Triangulation of polygons, triangulations on surfaces, Computational Geometry (cs.CG), FOS: Computer and information sciences, Graph of triangulations, Metric Geometry (math.MG), Edge flip, 68U05, edge flip, Mathematics - Metric Geometry, FOS: Mathematics, Computer Science - Computational Geometry, graph of triangulations, Triangulations on surfaces, triangulations of polygons

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