Existing VM placement schemes have measured their effectiveness solely by looking either Physical Machine's resources(CPU, memory) or network resource. However, real applications use all resource types to varying degrees. The result of applying existing placement schemes to VMs running real applications is a fragmented data center where resources along one dimension become unusable even though they are available because of the unavailability of resources along other dimensions. An example of this fragmentation is unusable CPU because of a bottlenecked network link from the physical machine which has available CPU. To date, evaluations of the efficacy of VM placement schemes has not recognized this fragmentation and it's ill effects, let alone try to measure it and avoid it. In this paper, we first define the notion of what we term "relative resource fragmentation" and illustrate how it can be measured in a data center. The metric we put forth for capturing the degree of fragmentation is comprehensive and includes all key data center resource types. We then propose a scheme of minimizing this fragmentation so as to maximize the availability of existing set of data center resources. Results of empirical evaluations of our placement scheme compared to existing network based placement schemes show a reduction of fragmentation by as much as 15% and increase in number of successfully placed applications by upto 20%.