2-connectivity and bipartite minors
Prove that for every integer $t$ there exists an integer $n$ such that every 2-connected graph on at least $n$ vertices has either a cycle of length at least $t$ or a $K_{2,t}$ minor.
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Prove that for every planar graph $G$ there exists an integer $k$ such that $G$ is isomorphic to a minor of the $k \times k$ grid.
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