Planar CPG graphs
Nicolas Champseix, Esther Galby, Bernard Ries

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 , there exists a planar graph which is -CPG but not -CPG. As a consequence, we obtain that -CPG is a strict subclass of -CPG.
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Taxonomy
TopicsAdvanced Graph Theory Research · Cell Adhesion Molecules Research · semigroups and automata theory
