A new obstruction for normal spanning trees

In a paper from 2001 (Journal of the LMS), Diestel and Leader offered proof that connected graph has normal spanning tree if only it no minor obtained canonically either an ( ℵ 0 , 1 ) -regular bipartite or order-theoretic Aronszajn tree. particular, this refuted earlier conjecture Halin's first these obstructions was needed to characterize graphs with trees. However, Leader's contains gap, their proposed list excluded minors is still not complete. paper, we construct third type obstruction: -sized without neither two types described by as minor. Further, show any forbidden characterising trees must contain arbitrarily large cardinality.