Orientations of infinite graphs with prescribed edge-connectivity

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• 作者：Carsten Thomassen
• 关键词：Mathematics Subject Classification (2000)05C40 ; 05C20
• 刊名：Combinatorica
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：36
• 期：5
• 页码：601-621
• 全文大小：386 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1439-6912
• 卷排序：36

文摘

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.