Vertex Spanning Planar Laman Graphs in Triangulated Surfaces

Eran Nevo; Simion Tarabykin

doi:10.1007/s00454-023-00517-w

Vertex Spanning Planar Laman Graphs in Triangulated Surfaces

Eran Nevo
, Simion Tarabykin

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We prove that every triangulation of either of the torus, projective plane and Klein bottle, contains a vertex-spanning planar Laman graph as a subcomplex. Invoking a result of Király, we conclude that every 1-skeleton of a triangulation of a surface of nonnegative Euler characteristic has a rigid realization in the plane using at most 26 locations for the vertices.

Original language	English
Pages (from-to)	912-927
Number of pages	16
Journal	Discrete and Computational Geometry
Volume	72
Issue number	2
DOIs	https://doi.org/10.1007/s00454-023-00517-w
State	Published - 1 Sep 2024
Externally published	Yes

Keywords

05C10
52C25
Framework rigidity
Rigidity with few locations
Triangulated surfaces

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-023-00517-w

Cite this

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abstract = "We prove that every triangulation of either of the torus, projective plane and Klein bottle, contains a vertex-spanning planar Laman graph as a subcomplex. Invoking a result of Kir{\'a}ly, we conclude that every 1-skeleton of a triangulation of a surface of nonnegative Euler characteristic has a rigid realization in the plane using at most 26 locations for the vertices.",

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AU - Tarabykin, Simion

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PY - 2024/9/1

Y1 - 2024/9/1

N2 - We prove that every triangulation of either of the torus, projective plane and Klein bottle, contains a vertex-spanning planar Laman graph as a subcomplex. Invoking a result of Király, we conclude that every 1-skeleton of a triangulation of a surface of nonnegative Euler characteristic has a rigid realization in the plane using at most 26 locations for the vertices.

AB - We prove that every triangulation of either of the torus, projective plane and Klein bottle, contains a vertex-spanning planar Laman graph as a subcomplex. Invoking a result of Király, we conclude that every 1-skeleton of a triangulation of a surface of nonnegative Euler characteristic has a rigid realization in the plane using at most 26 locations for the vertices.

KW - 05C10

KW - 52C25

KW - Framework rigidity

KW - Rigidity with few locations

KW - Triangulated surfaces

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ER -

Vertex Spanning Planar Laman Graphs in Triangulated Surfaces

Abstract

Keywords

ASJC Scopus subject areas

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