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The planar Cayley graphs are effectively enumerable I : consistently planar graphs
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Georgakopoulos, Agelos and Hamann, Matthias (2019) The planar Cayley graphs are effectively enumerable I : consistently planar graphs. Combinatorica, 39 . pp. 993-1019. doi:10.1007/s00493-019-3763-3
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Official URL: https://doi.org/10.1007/s00493-019-3763-3
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.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science > Mathematics | ||||||||
| Journal or Publication Title: | Combinatorica | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0209-9683 | ||||||||
| Official Date: | November 2019 | ||||||||
| Dates: |
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| Volume: | 39 | ||||||||
| Page Range: | pp. 993-1019 | ||||||||
| DOI: | 10.1007/s00493-019-3763-3 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Publisher Statement: | This is a post-peer-review, pre-copyedit version of an article published in Combinatorica. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00493-019-3763-3 | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
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| Open Access Version: |
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