Sublinear Separators in Intersection Graphs of Convex Shapes
Zdenĕk Dvořák, Rose McCarty, Sergey Norin · SIAM Journal on Discrete Mathematics · 2021
We give a natural sufficient condition for an intersection graph of compact convex sets in $\mathbb{R}^d$ to have a balanced separator of sublinear size. This condition generalizes several previous results on sublinear separators in intersection graphs. Furthermore, the argument used to prove the existence of sublinear separators is based on a connection with generalized coloring numbers which has not been previously explored in geometric settings.