Planar CPG graphs

TL;DR

The paper demonstrates that for each non-negative integer k, there are planar graphs that belong to the class B_{k+1}-CPG but not to B_k-CPG, establishing a strict hierarchy among these graph classes.

Contribution

It proves the existence of planar graphs that separate the classes B_k-CPG and B_{k+1}-CPG, showing the hierarchy is strict.

Findings

B_{k+1}-CPG properly contains B_k-CPG for all k

Existence of planar graphs in higher classes but not in lower

Hierarchy of CPG graph classes is strict

Abstract

We show that for any $k \geq 0$, there exists a planar graph which is $B_{k+1}$-CPG but not $B_k$-CPG. As a consequence, we obtain that $B_k$-CPG is a strict subclass of $B_{k+1}$-CPG.