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


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

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


  • Laman graph
  • rigidity
  • surface triangulation


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