Vertex spanning planar Laman graphs in triangulated surfaces
Combinatorics
2022-05-03 v1
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 Kir{\'a}ly, we conclude that every -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.
Keywords
Cite
@article{arxiv.2205.00558,
title = {Vertex spanning planar Laman graphs in triangulated surfaces},
author = {Eran Nevo and Simion Tarabykin},
journal= {arXiv preprint arXiv:2205.00558},
year = {2022}
}
Comments
18 pages, 11 figures, to be presented at FPSAC2022