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Is the shortest circuit/cocircuit problem on transversal matroids or gammoids NP-hard? Is there anything known about this? It is known that the shortest circuit on binary matroid is NP-hard. But I can not find any reference on transversal matroids or gammoids.

This is a followup question of A minimum set hitting every base of a matroid

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The shortest circuit problem for Transversal matroids is NP-hard, by a reduction from Clique. See Theorem 2.1 in "Reliable Assignments of Processors to Tasks and Factoring on Matroids" by Charles J. Colbourn and Ehab S. Elmallah ( http://citeseerx.ist.psu.edu/viewdoc/summary?doi= ).

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