Title: Minors of two-connected graphs of large path-width,
Abstract: Let $P$ be a graph with a vertex $v$ such that $P\backslash v$ 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. The proof is based on a new property
of tree-decompositions.