Groups, Geometry, and Dynamics
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Published online: 2010-10-15
On Leighton’s graph covering theoremWalter D. Neumann (1) Barnard College, Columbia University, New York, USA
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.
Keywords: Leighton’s theorem, graph covering, tree lattice
Neumann Walter: On Leighton’s graph covering theorem. Groups Geom. Dyn. 4 (2010), 863-872. doi: 10.4171/GGD/111