Characterising planar Cayley graphs and Cayley complexes in terms of group presentations
Group Theory
2015-03-17 v3 Combinatorics
Abstract
We prove that a Cayley graph can be embedded in the euclidean plane without accumulation points of vertices if and only if it is the 1-skeleton of a Cayley complex that can be embedded in the plane after removing redundant simplices. We also give a characterisation of these Cayley graphs in term of group presentations, and deduce that they can be effectively enumerated.
Keywords
Cite
@article{arxiv.1011.4255,
title = {Characterising planar Cayley graphs and Cayley complexes in terms of group presentations},
author = {Agelos Georgakopoulos},
journal= {arXiv preprint arXiv:1011.4255},
year = {2015}
}
Comments
This is the final version appearing in European J. Combin. This version contains many improvements to an earlier version of the paper appearing under the title "A group has a flat Cayley complex if and only if it has a VAP-free Cayley graph"