Graph minors. V. Excluding a planar graph

  title={Graph minors. V. Excluding a planar graph},
  author={N. Robertson and P. Seymour},
  journal={J. Comb. Theory, Ser. B},
  • N. Robertson, P. Seymour
  • Published 1986
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. B
  • 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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