Generating the cycle space of planar graphs

TL;DR

This paper proves that for certain planar graphs, the cycle space can be generated by an automorphism-invariant nested set of cycles, extending understanding of graph structure and symmetry.

Contribution

It introduces a method to generate the cycle space of planar 3-connected graphs using automorphism-invariant nested cycles, with insights into lower connectivity cases.

Findings

Cycle space generated by automorphism-invariant nested cycles

Applicable to finitely separable 3-connected planar graphs

Discussion on smaller connectivity cases

Abstract

We prove that the cycle space of every planar finitely separable 3-connected graph $G$ is generated by some ${\rm Aut}(G)$-invariant nested set of cycles. We also discuss the situation in the case of smaller connectivity.