Vertex Spanning Planar Laman Graphs in Triangulated Surfaces

Eran Nevo; Simion Tarabykin

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
Article number	#43
Journal	Seminaire Lotharingien de Combinatoire
Issue number	86
State	Published - 2022

Bibliographical note

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© 2022, Seminaire Lotharingien de Combinatoire. All Rights Reserved.

Keywords

Laman graph
rigidity
surface triangulation

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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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 - rigidity

KW - surface triangulation

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Vertex Spanning Planar Laman Graphs in Triangulated Surfaces

Abstract

Bibliographical note

Keywords

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