Abstract
We prove a decomposition result for locally finite graphs which can be used to extend results on edge-connectivity from finite to infinite graphs. It implies that every 4k-edge-connected graph G contains an immersion of some finite 2k-edge-connected Eulerian graph containing any prescribed vertex set (while planar graphs show that G need not containa subdivision of a simple finite graph of large edge-connectivity). Also, every 8k-edge connected infinite graph has a k-arc-connected orientation, as conjectured in 1989.
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Research partly supported by ERC Advanced Grant GRACOL.
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Thomassen, C. Orientations of infinite graphs with prescribed edge-connectivity. Combinatorica 36, 601–621 (2016). https://doi.org/10.1007/s00493-015-3173-0
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DOI: https://doi.org/10.1007/s00493-015-3173-0