Every graph of large rank-depth contains a pivot-minor isomorphic to a long path or to two cliques joined by a half-graph, resolving a 2021 conjecture.
Pascal Gollin, Kevin Hendrey, Dillon Mayhew, and Sang-il Oum, Obstructions for bounded branch-depth in matroids , Adv
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Unavoidable pivot-minors in graphs of large rank-depth
Every graph of large rank-depth contains a pivot-minor isomorphic to a long path or to two cliques joined by a half-graph, resolving a 2021 conjecture.