# Graph minors. V. Excluding a planar graph

@article{Robertson1986GraphMV, title={Graph minors. V. Excluding a planar graph}, author={N. Robertson and P. Seymour}, journal={J. Comb. Theory, Ser. B}, year={1986}, volume={41}, pages={92-114} }

We prove that for every planar graph H there is a number w such that every graph with no minor isomorphic to H can be constructed from graphs with at most w vertices, by piecing them together in a tree structure. This has several consequences; for example, it implies that: (i) if A is a set of graphs such that no member is isomorphic to a minor of another, and some member of A is planar, then A is finite; (ii) for every fixed planar graph H there is a polynomial time algorithm to test if an… CONTINUE READING

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