All Graphs Have Tree-Decompositions Displaying Their Topological Ends

Abstract

We show that every connected graph has a spanning tree that displays all its topological ends. This proves a 1964 conjecture of Halin in corrected form, and settles a problem of Diestel from 1992.

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Acknowledgement

I thank two anonymous referees whose valuable comments improved this paper. Furthermore, I thank Nathan Bowler for pointing out an error in an earlier version.

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Correspondence to Johannes Carmesin.

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Carmesin, J. All Graphs Have Tree-Decompositions Displaying Their Topological Ends. Combinatorica 39, 545–596 (2019). https://doi.org/10.1007/s00493-018-3572-0

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Mathematics Subject Classification (2010)

  • 05C63
  • 05B35