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The fundamental group of a locally finite graph with ends

We characterize the fundamental group of a locally finite graph $G$
with ends, by embedding it canonically as a subgroup in the inverse
limit of the free groups $\pi_1(G')$ with $G'\sub G$ finite. As an
intermediate step, we characterize $\pi_1(|G|)$ combinatorially as a
group of infinite words.
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