We prove that the cycle space of every planar finitely separable 3-connected graph G is generated by some Aut(G)-invariant nested set of cycles. We also discuss the situation in the case of smaller connectivity.
@article{arxiv.1411.6392,
title = {Generating the cycle space of planar graphs},
author = {Matthias Hamann},
journal= {arXiv preprint arXiv:1411.6392},
year = {2014}
}