Graph minors XXIII. Nash-Williams' immersion conjecture

@article{Robertson2010GraphMX,
  title={Graph minors XXIII. Nash-Williams' immersion conjecture},
  author={Neil Robertson and Paul D. Seymour},
  journal={J. Comb. Theory, Ser. B},
  year={2010},
  volume={100},
  pages={181-205}
}
We define a quasi-order of the class of all finite hypergraphs, and prove it is a well-quasi-order. This has two corollaries of interest: • Wagner’s conjecture, proved in a previous paper, states that for every infinite set of finite graphs, one of its members is a minor of another. The present result implies the same conclusion even if the vertices or edges of the graphs are labelled from a well-quasi-order and we require the minor relation to respect the labels. • Nash-Williams’ “immersion… CONTINUE READING
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On well-quasi-ordering trees

  • C. St. J.A. Nash-Williams
  • Theory of Graphs and Its Applications (Proc. Symp…
  • 1963
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On wellquasiordering trees ” , Theory of Graphs and Its Applications ( Proc

  • C. St. J. A. Nash-Williams
  • Symp . Smolenice , 1963 ) , Publ . House…
  • 1964

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