Abstract
Several results concerning contractible and removable edges in 3-connected finite graphs are extended to infinite graphs. First, we prove that every 3-connected locally finite infinite graph has infinitely many removable edges. Next, we prove that for any 3-connected graph $$G$$G, if $$x$$x is a finite degree vertex in $$G$$G and is not incident to any contractible edges, then $$G-x$$G-x is a finite cycle or contains a border pair. As a result, every 3-connected locally finite infinite graph contains infinitely many contractible edges. Lastly, it is shown that for any 3-connected locally finite infinite graph $$G$$G which is triangle-free or has minimum degree at least 4, the closure of the subgraph induced by all the contractible edges in the Freudenthal compactification of $$G$$G is topologically 2-connected.
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