The robust recoverable spanning tree problem with interval costs is   polynomially solvable
  In this paper the robust recoverable spanning tree problem with interval edge costs is considered. The complexity of this problem has remained open to date. It is shown that the problem is polynomially solvable, by using an iterative relaxation method. A generalization of this idea to the robust recoverable matroid basis problem is also presented. Polynomial algorithms for both robust recoverable problems are proposed. 
Mikita Hradovich, Adam Kasperski, Pawel Zielinski
cs.DS