Vertex Spanning Planar Laman Graphs in Triangulated Surfaces

Eran Nevo*, Simion Tarabykin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageAmerican English
Article number#43
JournalSeminaire Lotharingien de Combinatoire
Issue number86
StatePublished - 2022

Bibliographical note

Funding Information:
*nevo@math.huji.ac.il. Partially supported by the Israel Science Foundation grants ISF-1695/15 and ISF-2480/20 and by ISF-BSF joint grant 2016288. †simon.trabykin@gmail.com. Partially supported by ISF grant 1695/15.

Publisher Copyright:
© 2022, Seminaire Lotharingien de Combinatoire. All Rights Reserved.

Keywords

  • Laman graph
  • rigidity
  • surface triangulation

Fingerprint

Dive into the research topics of 'Vertex Spanning Planar Laman Graphs in Triangulated Surfaces'. Together they form a unique fingerprint.

Cite this