In Oxley's Matroid Theory, Problem 14.8.5, it states that it is (or at least was in 1992) an open problem to determine when the dual matroid of a transversal matroid is also transversal. I had assumed that this did not hold for all transversal matroids, however I've had trouble finding an example of a transversal matroid whose dual is not transversal. Are the known examples of such matroids, and could someone point me towards one?
2026-03-26 11:06:53.1774523213
A transversal matroid whose dual is not transversal
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