Abstract The proposed approach is based on standard graph transduction, semi-supervised learning (SSL) framework. Its key novelty is the integration of global connectivity constraints into this framework. Although connectivity leads to higher order constraints and their number is an exponential, fifinding the most violated connectivity constraint can be done effificiently in polynomial time. Moreover, each such constraint can be represented as a linear inequality. Based on this fact, we design a cutting-plane algorithm to solve the integrated problem. It iterates between solving a convex quadratic problem of label propagation with linear inequality constraints, and fifinding the most violated constraint. We demonstrate the benefifits of the proposed approach on a realistic and very challenging problem of cosegmentation of multiple foreground objects in photo collections in which the foreground objects are not present in all photos. The obtained results not only demonstrate performance boost induced by the connectivity constraints, but also show a signifificant improvement over the state-of-the-art methods.