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|
|Journal||Seminaire Lotharingien de Combinatoire|
|State||Published - 2022|
Bibliographical noteFunding Information:
*firstname.lastname@example.org. Partially supported by the Israel Science Foundation grants ISF-1695/15 and ISF-2480/20 and by ISF-BSF joint grant 2016288. †email@example.com. Partially supported by ISF grant 1695/15.
© 2022, Seminaire Lotharingien de Combinatoire. All Rights Reserved.
- Laman graph
- surface triangulation