Due to the limited environments of radio frequency resources, the frequency assignment problem (FAP) is a crucial issue. We especially focus on the system that requires re-assignment of the frequencies often, so that the operation time is a limited resource as well as the radio resource. The FAP is closely related to the graph coloring problem, which is NP-hard problem. In this paper, we investigate a frequency assignment problem from a graph theory perspective for those limited system. We propose an effective algorithm based on the graph coloring theory and randomization incorporation into greedy heuristics. Main concern of the frequency assignments to clustered nodes is to reduce the number of used frequencies and the range. This paper has its another novelty in considering realistic interference constraints by considering net filter discrimination and measurement data from the field. Performance analysis is done by synthetic and measured data, and we observe a significant improvements by employing proposed algorithms in both cases.