A linear bound for the Colin de Verdière parameter $\mu$ for graphs embedded on surfaces

Abstract

We provide a combinatorial and self-contained proof that for all graphs $G$ embedded on a surface $S$, the Colin de Verdière parameter $\mu (G)$ is upper bounded by $7-2\chi (S)$.

References in corpus (1)

• Discrete surfaces with length and area and minimal fillings of the circle