It is known that intersection of three general matroids is NP-hard (source), which is done via reduction from Hamiltonian cycle. The reduction uses one graphic matroid and two connectivity matroids.
A special case of a problem I am working on can be solved by intersection multiple graphic matroids, but I haven't been able to find, whether this problem is in P.
Question: Is it known? Can someone please refer me to a paper or something?
(Note: I have asked this question on Computer Science and was referred here.)