## Graph minors. IV: Tree-width and well-quasi-ordering.(English)Zbl 0719.05032

[Part III, cf. ibid. 36, 49-64 (1984; Zbl 0548.05025.]
The famous conjecture of K. Wagner says that if $$G_ 1,G_ 2,..$$. is any countably infinite sequence of finite graphs, then there exist $$i,j,j>i\geq 1$$ such that $$G_ i$$ is isomorphic to a minor of $$G_ j$$. By a result of Kruskal, this is true if all the $$G_ i's$$ are trees. The authors extend Kruskal’s theorem to all sequences in which the first member $$G_ 1$$ is planar. This is one of the steps towards establishing the truth of Wagner’s conjecture in general.

### MSC:

 05C10 Planar graphs; geometric and topological aspects of graph theory

### Keywords:

graph minor; tree-width; Wagner’s conjecture

Zbl 0548.05025
Full Text:

### References:

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