Vertex Spanning Planar Laman Graphs in Triangulated Surfaces

Eran Nevo*, Simion Tarabykin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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
JournalDiscrete and Computational Geometry
StateAccepted/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.


  • Framework rigidity
  • Rigidity with few locations
  • Triangulated surfaces


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