With the increasing cost of maintaining IT centers, organizations are looking into outsourcing thier storage and computational needs to a cloud server. However, such outsourcing has also raised the more serious issue of data privacy. In this paper, we summarize our work in privacy-preserving data outsourcing. In particular, we discuss the issue of employing vertical fragmentation to a relation so that the fragment that is assigned to the cloud server contains maximum data without violating privacy. Here, privacy is expressed in terms of a set of confidentiality constraints. We represent the confidentiality constraints as a graph where the nodes are the attributes and links represent paired confidentiality. We then apply the graph coloring problem with two colors for the a cyclic portion of the graph. We use some heuristic to eliminate the cycles, and complete the coloring of all nodes. We are currently extending the work to multiple relations and constraints with multiple attributes in a constraint (i.e., triplet, quadruplet, etc.) instead of just pairs.