Planar Transitive Graphs

  • Matthias Hamann Alfred Renyi Institute of Mathematics, Budapest
Keywords: Planar graphs, Transitive graphs, Cycles


We prove that the first homology group of every planar locally finite transitive graph $G$ is finitely generated as an $\Aut(G)$-module and we prove a similar result for the fundamental group of locally finite planar Cayley graphs. Corollaries of these results include Droms's theorem that planar groups are finitely presented and Dunwoody's theorem that planar locally finite transitive graphs are accessible.

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