We consider the problem of information collection from a polygonal environment using a multi-robot system, subject to continuous connectivity constraints. In particular, the robots, having a common radius of communication range, must remain connected throughout the exploration maximizing the information collection. The information gained through the exploration of the terrain is wirelessly transmitted to a base station. The base station performs the centralized planning of informative paths for the robots based on the information collected by them and thereafter, the robots follow these paths. This paper formulates the problem of multi-robot informative path planning under continuous connectivity constraints as an integer program leveraging the ideas of bipartite graph matching and minimal node separators. Theoretical analysis of the proposed solution proves that the informative paths will be collision-free and will be free of both livelock and deadlock. Experimental results demonstrate the low computational requirements of our algorithm for planning the informative paths, taking only about 0.75 sec. for planning a joint set of collision-free informative locations for 10 robots.