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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

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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
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:
DateEvent
November 2019Published
2 October 2019Available
8 November 2018Accepted
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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