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-isometry invariant when cosets are preserved.
arXiv preprint arXiv:0708.0920 , year=
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
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.
verdicts
UNVERDICTED 3representative citing papers
Connected locally finite quasi-transitive graphs quasi-isometric to planar graphs are accessible, classifying such finitely generated groups as virtually free products of free and surface groups that admit planar Cayley graphs.
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.
citing papers explorer
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Relative accessibility for graphs
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-isometry invariant when cosets are preserved.
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Accessibility, planar graphs, and quasi-isometries
Connected locally finite quasi-transitive graphs quasi-isometric to planar graphs are accessible, classifying such finitely generated groups as virtually free products of free and surface groups that admit planar Cayley graphs.
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Almost planar finitely presented groups
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.