Integer Linear Programming (ILP) formulations of Markov random fields (MRFs) models with global connectivity priors were investigated previously in computer vision, e.g., [1,2]. In these works, only Linear Programing (LP) relaxations [1,2] or simplified versions [3] of the problem were solved. This paper investigates the ILP of multi-label MRF with exact connectivity priors via a branch-and-cut method, which provably finds globally optimal solutions. The method enforces connectivity priors iteratively by a cutting plane method, and provides feasible solutions with a guarantee on sub-optimality even if we terminate it earlier. The proposed ILP can be applied as a post-processing method on top of any existing multi-label segmentation approach. As it provides globally optimal solution, it can be used off-line to generate ground-truth labeling, which serves as quality check for any fast on-line algorithm. Furthermore, it can be used to generate groundtruth proposals for weakly supervised segmentation.