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arxiv: 0708.0920 · v2 · submitted 2007-08-07 · 🧮 math.GR

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Planar graphs and covers

M. J. Dunwoody
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classification 🧮 math.GR
keywords graphsplanarfinitegraphgroupalmostautomorphismsbuilt
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Planar locally finite graphs which are almost vertex transitive are discussed. If the graph is 3-connected and has at most one end then the group of automorphisms is a planar discontinuous group and its structure is well-known. A general result is obtained for such graphs where no restriction is put on the number of ends. It is shown that such a graph can be built up from one ended or finite planar graphs in a precise way. The results give a classification of the finitely generated groups with planar Cayley graphs.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Relative accessibility for graphs

    math.CO 2026-05 unverdicted novelty 7.0

    Relative accessibility in graphs is defined relative to peripheral systems, characterized via Boolean ring subrings for quasi-transitive graphs, and shown to match the group-theoretic version while being quasi-isometr...

  2. Almost planar finitely presented groups

    math.GR 2026-05 unverdicted novelty 7.0

    Finitely presented groups with k-planar Cayley graphs have finite-index subgroups with planar Cayley graphs; k-planar coarsely simply connected quasi-transitive graphs are quasi-isometric to planar graphs.