Geodesic
On Leighton’s graph covering theorem
Walter D. Neumann1
1Barnard College, Columbia University, New York, USA
Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 863-872

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DOI

We give short expositions of both Leighton’s proof and the Bass–Kulkarni proof of Leighton’s graph covering theorem, in the context of colored graphs. We discuss a further generalization, needed elsewhere, to “symmetry-restricted graphs”. We can prove it in some cases, for example, if the “graph of colors” is a tree, but we do not know if it is true in general. We show that Bass’s Conjugation Theorem, which is a tool in the Bass–Kulkarni approach, does hold in the symmetry-restricted context.
DOI : 10.4171/ggd/111
Classification : 20-XX, 05-XX, 00-XX
Mots-clés : Leighton’s theorem, graph covering, tree lattice

Walter D. Neumann  1

1 Barnard College, Columbia University, New York, USA 
Walter D. Neumann. On Leighton’s graph covering theorem. Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 863-872. doi: 10.4171/ggd/111
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