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Graph minors. XX: Wagner’s conjecture. (English) Zbl 1061.05088
This paper is the culmination of a series investigating graph minors. In this work the authors prove Wagner’s conjecture: every infinite set of finite graphs contains one graph that is isomorphic to a minor of another. As a corollary: for every class of finite graphs closed under taking minors, there is a finite list of excluded minors characterizing that class.
The result is of fundamental importance in graph theory.

MSC:
05C83 Graph minors
05C65 Hypergraphs
05C10 Planar graphs; geometric and topological aspects of graph theory
57M15 Relations of low-dimensional topology with graph theory
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[2] Robertson, N.; Seymour, P.D., Graph minors. X. obstructions to tree-decomposition, J. combin. theory ser. B, 52, 153-190, (1991) · Zbl 0764.05069
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