Determining strong base-orderability of a matroid

https://mathoverflow.net/questions/194006/determining-strong-base-orderability-of-a-matroid

determining base-orderability of a matroid can be done through finding perfect matching in a bipartite graph with edges. call oracle times to build the graph and run a matching algorithm.

Is the union of strongly base-orderable matroids strongly base-orderable? yes. https://mathoverflow.net/questions/201101/is-the-union-of-strongly-base-orderable-matroids-strongly-base-orderable also see wikipedia

difference between base-orderable and strong base orderable?

https://arxiv.org/abs/1507.05521

an induction on the size of the set

1-BO
2-BO
…
-BO = SBO

given 2 bases of a matroid and a k-BO bijection f, find subsets with k+1 elements which do satisfy -BO?

1-BO -> 2-BO is already hard…