English

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 11-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

R2 v1 2026-06-24T11:04:04.728Z