Inventiones mathematicae

, Volume 108, Issue 1, pp 131–162 | Cite as

A proof of the bounded graph conjecture

  • Reinhard Diestel
  • Imre Leader


An infinite graph is called bounded if for every labelling of its vertices with natural numbers there exists a sequence of natural numbers which eventually exceeds the labelling along any ray in the graph. We prove an old conjecture of Halin, which characterizes the bounded graphs in terms of four forbidden topological subgraphs.


Natural Number Infinite Graph Bounded Graph Topological Subgraph 
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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Reinhard Diestel
    • 1
  • Imre Leader
    • 2
  1. 1.Faculty of Mathematics, (SFB343)Bielefeld UniversityBielefeldGermany
  2. 2.Department of Pure MathematicsCambridgeEngland

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