Orientations of infinite graphs with prescribed edge-connectivity |
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Authors: | Carsten Thomassen |
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Institution: | 1.Department of Applied Mathematics and Computer Science,Technical University of Denmark,Lyngby,Denmark |
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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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