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Orientations of infinite graphs with prescribed edge-connectivity. (English) Zbl 1399.05139
Summary: 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 contain a 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 by the author [in: Combinatorial mathematics: Proceedings of the third international conference, held in New York, USA, June 10–14, 1985. New York: New York Academy of Sciences. 402–412 (1989; Zbl 0709.05030)].

##### MSC:
 05C40 Connectivity 05C20 Directed graphs (digraphs), tournaments 05C63 Infinite graphs 05C45 Eulerian and Hamiltonian graphs
##### Keywords:
finite graphs; edge-connectivity; infinite graphs
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##### References:
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