Vertex Spanning Planar Laman Graphs in Triangulated Surfaces

Eran Nevo; Simion Tarabykin

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
Article number	#43
Journal	Seminaire Lotharingien de Combinatoire
Issue number	86
State	Published - 1 Jan 2022
Externally published	Yes

Keywords

Laman graph
rigidity
surface triangulation

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Cite this

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title = "Vertex Spanning Planar Laman Graphs in Triangulated Surfaces",

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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T1 - Vertex Spanning Planar Laman Graphs in Triangulated Surfaces

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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 - Laman graph

KW - rigidity

KW - surface triangulation

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M3 - Article

AN - SCOPUS:85161519310

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JO - Seminaire Lotharingien de Combinatoire

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IS - 86

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ER -

Vertex Spanning Planar Laman Graphs in Triangulated Surfaces

Abstract

Keywords

ASJC Scopus subject areas

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