Characterising planar Cayley graphs and Cayley complexes in terms of group presentations

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.

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"

References in corpus (1)

• Planar graphs and covers

Cited by in corpus (4)

• The feasible region for consecutive patterns of permutations is a cycle polytope
• Triangulations of simplices with vanishing local h-polynomial
• Splitting groups with cubic Cayley graphs of connectivity two
• Curvature, geometry and spectral properties of planar graphs