Contractible and Removable Edges in 3-Connected Infinite Graphs

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 , if is a finite degree vertex in and is not incident to any contractible edges, then 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 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 is topologically 2-connected.