English

A linear bound for the Colin de Verdi\`ere parameter $\mu$ for graphs embedded on surfaces

Combinatorics 2023-03-20 v2 Computational Geometry

Abstract

We provide a combinatorial and self-contained proof that for all graphs GG embedded on a surface SS, the Colin de Verdi\`ere parameter μ(G)\mu(G) is upper bounded by 72χ(S)7-2\chi(S).

Cite

@article{arxiv.2303.00556,
  title  = {A linear bound for the Colin de Verdi\`ere parameter $\mu$ for graphs embedded on surfaces},
  author = {Camille Lanuel and Francis Lazarus and Rudi Pendavingh},
  journal= {arXiv preprint arXiv:2303.00556},
  year   = {2023}
}
R2 v1 2026-06-28T08:54:19.527Z