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.
Cite this article
Walter D. Neumann, On Leighton’s graph covering theorem. Groups Geom. Dyn. 4 (2010), no. 4, pp. 863–872DOI 10.4171/GGD/111