Minors of two-connected graphs of large path-width

12/12/2017

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by   Thanh N. Dang, et al.

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Let P be a graph with a vertex v such that P v is a forest, and let Q be an outerplanar graph. We prove that there exists a number p=p(P,Q) such that every 2-connected graph of path-width at least p has a minor isomorphic to P or Q. This result answers a question of Seymour and implies a conjecture of Marshall and Wood.