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.
Original language | English |
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Journal | Combinatorica |
Volume | 36 |
Issue number | 5 |
Pages (from-to) | 601–621 |
Number of pages | 21 |
ISSN | 0209-9683 |
DOIs | |
Publication status | Published - 2016 |