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 | American English |
|---|---|
| Article number | #43 |
| Journal | Seminaire Lotharingien de Combinatoire |
| Issue number | 86 |
| State | Published - 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