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

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	American English
Journal	Discrete and Computational Geometry
DOIs	https://doi.org/10.1007/s00454-023-00517-w
State	Accepted/In press - 2023

Bibliographical note

Funding Information:
Eran Nevo was partially supported by the Israel Science Foundation grants ISF-1695/15 and ISF-2480/20 and by ISF-BSF joint grant 2016288. Simion Tarabykin was partially supported by ISF grant 1695/15.

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

Keywords

Framework rigidity
Rigidity with few locations
Triangulated surfaces

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10.1007/s00454-023-00517-w

Cite this

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note = "Funding Information: Eran Nevo was partially supported by the Israel Science Foundation grants ISF-1695/15 and ISF-2480/20 and by ISF-BSF joint grant 2016288. Simion Tarabykin was partially supported by ISF grant 1695/15. Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Tarabykin, Simion

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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 - Framework rigidity

KW - Rigidity with few locations

KW - Triangulated surfaces

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DO - 10.1007/s00454-023-00517-w

M3 - Article

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JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

ER -

Vertex Spanning Planar Laman Graphs in Triangulated Surfaces

Abstract

Bibliographical note

Keywords

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