On Well-Quasi-Ordering Finite Trees

  • C. ST. J. A. Nash-Williams
Part of the Modern Birkhäuser Classics book series (MBC)


A new and simple proof is given of the known theorem that, if T 1 , T 2, … , is an infinite sequence of finite trees, then there exist i and j such that i < j and T i is homeomorphic to a subtree of T j.


Simple Proof Research Note Infinite Sequence Cardinal Number Cartesian Product Versus 
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  1. (1).
    Higman. G. Ordering by divisibility in abstract algebras. Proc. London Math. Soc. (3), 2 (1952), 326–336.Google Scholar
  2. (2).
    Kruskal,. J. B. Well-quasi-ordering, the tree theorem, and Vázsony’s conjecture. Trans. American Math. Soc. 95 (1960). 210–225.MATHMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • C. ST. J. A. Nash-Williams
    • 1
  1. 1.King’s CollegeAberdeenUSA

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