It is known that intersection of three general matroids is NP-hard ([source](https://en.wikipedia.org/wiki/Matroid_intersection)), 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](https://cs.stackexchange.com/questions/75228/is-intersection-of-k-3-graphic-matroids-in-p) and was referred here.)