  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.
