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arXiv · 0906.2496

On Leighton's graph covering theorem

Walter D. Neumann
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Abstract

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.

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Walter D. Neumann. 2009-06-13. On Leighton's graph covering theorem. https://arxiv.org/abs/0906.2496

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