The planar Cayley graphs are effectively enumerable I: consistently planar graphs
Combinatorics
2019-01-04 v3 Group Theory
Abstract
We obtain an effective enumeration of the family of finitely generated groups admitting a faithful, properly discontinuous action on some 2-manifold contained in the sphere. This is achieved by introducing a type of group presentation capturing exactly these groups. Extending this in a companion paper, we find group presentations capturing the planar finitely generated Cayley graphs. Thus we obtain an effective enumeration of these Cayley graphs, yielding in particular an affirmative answer to a question of Droms et al.
Cite
@article{arxiv.1506.03361,
title = {The planar Cayley graphs are effectively enumerable I: consistently planar graphs},
author = {Agelos Georgakopoulos and Matthias Hamann},
journal= {arXiv preprint arXiv:1506.03361},
year = {2019}
}
Comments
To appear in Combinatorica. The second half of the previous version is arXiv:1901.00347