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

^*Corresponding author for this work

Einstein Institute of Mathematics

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 - Sep 2024

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.

Keywords

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

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10.1007/s00454-023-00517-w

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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.

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KW - Framework rigidity

KW - Rigidity with few locations

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ER -

Vertex Spanning Planar Laman Graphs in Triangulated Surfaces

Abstract

Bibliographical note

Keywords

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