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Let a be an integer. It is proved that for any s and k, there exists a constant N=N(s,k,a) such that every 312(a+1)-connected graph with at least N vertices either contains a subdivision of Ka,sk or a minor isomorphic to s disjoint copies of Ka,k. In fact, we prove that connectivity 3a+2 and minimum degree at least 312(a+1)−3 are enough while the other conditions cannot be weakened.When s=1 and k=a,...
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