Geodesic
Planar transitive graphs
Matthias Hamann1
1Alfred Renyi Institute of Mathematics, Budapest
The electronic journal of combinatorics, Tome 25 (2018) no. 4
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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.
DOI : 10.37236/7888
Classification : 05C10, 05C25, 05C38
Mots-clés : planar graphs, transitive graphs, cycles

Matthias Hamann  1

1 Alfred Renyi Institute of Mathematics, Budapest 
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Matthias Hamann. Planar transitive graphs. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/7888

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