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